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Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: slsqp.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Sequential Quadratic Programming. # # CHANGELOG # # 2023-02-09: Direct Jacobian now converges to proper value so removing # confusing commentary in example. Also Cleanup and tweaks for safety and # efficiency (Avraham Adler) # 2024-06-04: Switched desired direction of the hin/hinjac inequalities, leaving # the old behavior as the default for now. Also cleaned up the HS100 # example (Avraham Adler). # #' Sequential Quadratic Programming (SQP) #' #' Sequential (least-squares) quadratic programming (SQP) algorithm for #' nonlinearly constrained, gradient-based optimization, supporting both #' equality and inequality constraints. #' #' The algorithm optimizes successive second-order (quadratic/least-squares) #' approximations of the objective function (via BFGS updates), with #' first-order (affine) approximations of the constraints. #' #' @param x0 starting point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param gr gradient of function \code{fn}; will be calculated numerically if #' not specified. #' @param lower,upper lower and upper bound constraints. #' @param hin function defining the inequality constraints, that is #' \code{hin <= 0} for all components. This is new behavior in line with the #' rest of the \code{nloptr} arguments. To use the old behavior, please set #' \code{deprecatedBehavior} to \code{TRUE}. #' @param hinjac Jacobian of function \code{hin}; will be calculated #' numerically if not specified. #' @param heq function defining the equality constraints, that is \code{heq = 0} #' for all components. #' @param heqjac Jacobian of function \code{heq}; will be calculated #' numerically if not specified. #' @param nl.info logical; shall the original NLopt info been shown. #' @param control list of options, see \code{nl.opts} for help. #' @param deprecatedBehavior logical; if \code{TRUE} (default for now), the old #' behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} #' instead of \eqn{\le 0}. This will be reversed in a future release and #' eventually removed. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 1) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export slsqp #' #' @author Hans W. Borchers #' #' @note See more infos at #' \url{https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/}. #' #' @seealso \code{alabama::auglag}, \code{Rsolnp::solnp}, #' \code{Rdonlp2::donlp2} #' #' @references Dieter Kraft, ``A software package for sequential quadratic #' programming'', Technical Report DFVLR-FB 88-28, Institut fuer Dynamik der #' Flugsysteme, Oberpfaffenhofen, July 1988. #' #' @examples #' #' ## Solve the Hock-Schittkowski problem no. 100 with analytic gradients #' ## See https://apmonitor.com/wiki/uploads/Apps/hs100.apm #' #' x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) #' fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + #' 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + #' x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} #' #' hin.hs100 <- function(x) {c( #' 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, #' 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, #' 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, #' 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - #' 11 * x[7]) #' } #' #' S <- slsqp(x0.hs100, fn = fn.hs100, # no gradients and jacobians provided #' hin = hin.hs100, #' nl.info = TRUE, #' control = list(xtol_rel = 1e-8, check_derivatives = TRUE), #' deprecatedBehavior = FALSE) #' #' ## The optimum value of the objective function should be 680.6300573 #' ## A suitable parameter vector is roughly #' ## (2.330, 1.9514, -0.4775, 4.3657, -0.6245, 1.0381, 1.5942) #' #' S #' slsqp <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, heq = NULL, heqjac = NULL, nl.info = FALSE, control = list(), deprecatedBehavior = TRUE, ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LD_SLSQP" fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (is.null(gr)) { gr <- function(x) nl.grad(x, fn) } else { .gr <- match.fun(gr) gr <- function(x) .gr(x, ...) } if (!is.null(hin)) { if (deprecatedBehavior) { warning("The old behavior for hin >= 0 has been deprecated. Please ", "restate the inequality to be <=0. The ability to use the old ", "behavior will be removed in a future release.") .hin <- match.fun(hin) hin <- function(x) -.hin(x, ...) # change hin >= 0 to hin <= 0 ! } if (is.null(hinjac)) { hinjac <- function(x) nl.jacobian(x, hin) } else if (deprecatedBehavior) { warning("The old behavior for hinjac >= 0 has been deprecated. Please ", "restate the inequality to be <=0. The ability to use the old ", "behavior will be removed in a future release.") .hinjac <- match.fun(hinjac) hinjac <- function(x) -.hinjac(x) } } if (!is.null(heq)) { .heq <- match.fun(heq) heq <- function(x) .heq(x) if (is.null(heqjac)) { heqjac <- function(x) nl.jacobian(x, heq) } else { .heqjac <- match.fun(heqjac) heqjac <- function(x) .heqjac(x) } } S0 <- nloptr(x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, eval_g_ineq = hin, eval_jac_g_ineq = hinjac, eval_g_eq = heq, eval_jac_g_eq = heqjac, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/ccsaq.R0000644000176200001440000001403114634272373013220 0ustar liggesusers# SPDX-License-Identifier: LGPL-3.0-or-later # File: ccsaq.R # Author: Julien Chiquet # Date: 02 October 2018 # # Wrapper to solve optimization problem using CCSAQ. # # CHANGELOG: # 2023-02-11: Tweaks for efficiency and readability (Avraham Adler) # 2024-06-04: Switched desired direction of the hin/hinjac inequalities, leaving # the old behavior as the default for now. Also cleaned up the HS100 # example (Avraham Adler). # #' Conservative Convex Separable Approximation with Affine Approximation plus #' Quadratic Penalty #' #' This is a variant of CCSA ("conservative convex separable approximation") #' which, instead of constructing local MMA approximations, constructs simple #' quadratic approximations (or rather, affine approximations plus a quadratic #' penalty term to stay conservative) #' #' @param x0 starting point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param gr gradient of function \code{fn}; will be calculated numerically if #' not specified. #' @param lower,upper lower and upper bound constraints. #' @param hin function defining the inequality constraints, that is #' \code{hin>=0} for all components. #' @param hinjac Jacobian of function \code{hin}; will be calculated #' numerically if not specified. #' @param nl.info logical; shall the original NLopt info been shown. #' @param control list of options, see \code{nl.opts} for help. #' @param deprecatedBehavior logical; if \code{TRUE} (default for now), the old #' behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} #' instead of \eqn{\le 0}. This will be reversed in a future release and #' eventually removed. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 1) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export ccsaq #' #' @note ``Globally convergent'' does not mean that this algorithm converges to #' the global optimum; it means that it is guaranteed to converge to some local #' minimum from any feasible starting point. #' #' @seealso \code{\link{mma}} #' #' @references Krister Svanberg, ``A class of globally convergent optimization #' methods based on conservative convex separable approximations,'' SIAM J. #' Optim. 12 (2), p. 555-573 (2002). #' #' @examples #' #' ## Solve the Hock-Schittkowski problem no. 100 with analytic gradients #' ## See https://apmonitor.com/wiki/uploads/Apps/hs100.apm #' #' x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) #' fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + #' 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + #' x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} #' #' hin.hs100 <- function(x) {c( #' 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, #' 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, #' 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, #' 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - #' 11 * x[7]) #' } #' #' gr.hs100 <- function(x) { #' c( 2 * x[1] - 20, #' 10 * x[2] - 120, #' 4 * x[3] ^ 3, #' 6 * x[4] - 66, #' 60 * x[5] ^ 5, #' 14 * x[6] - 4 * x[7] - 10, #' 4 * x[7] ^ 3 - 4 * x[6] - 8) #' } #' #' hinjac.hs100 <- function(x) { #' matrix(c(4 * x[1], 12 * x[2] ^ 3, 1, 8 * x[4], 5, 0, 0, #' 7, 3, 20 * x[3], 1, -1, 0, 0, #' 23, 2 * x[2], 0, 0, 0, 12 * x[6], -8, #' 8 * x[1] - 3 * x[2], 2 * x[2] - 3 * x[1], 4 * x[3], 0, 0, 5, -11), #' nrow = 4, byrow = TRUE) #' } #' #' ## The optimum value of the objective function should be 680.6300573 #' ## A suitable parameter vector is roughly #' ## (2.330, 1.9514, -0.4775, 4.3657, -0.6245, 1.0381, 1.5942) #' #' # Results with exact Jacobian #' S <- ccsaq(x0.hs100, fn.hs100, gr = gr.hs100, #' hin = hin.hs100, hinjac = hinjac.hs100, #' nl.info = TRUE, control = list(xtol_rel = 1e-8), #' deprecatedBehavior = FALSE) #' #' # Results without Jacobian #' S <- ccsaq(x0.hs100, fn.hs100, hin = hin.hs100, #' nl.info = TRUE, control = list(xtol_rel = 1e-8), #' deprecatedBehavior = FALSE) #' ccsaq <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, nl.info = FALSE, control = list(), deprecatedBehavior = TRUE, ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LD_CCSAQ" fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (is.null(gr)) { gr <- function(x) nl.grad(x, fn) } else { .gr <- match.fun(gr) gr <- function(x) .gr(x, ...) } if (!is.null(hin)) { if (deprecatedBehavior) { warning("The old behavior for hin >= 0 has been deprecated. Please ", "restate the inequality to be <=0. The ability to use the old ", "behavior will be removed in a future release.") .hin <- match.fun(hin) hin <- function(x) -.hin(x, ...) # change hin >= 0 to hin <= 0 ! } if (is.null(hinjac)) { hinjac <- function(x) nl.jacobian(x, hin) } else if (deprecatedBehavior) { warning("The old behavior for hinjac >= 0 has been deprecated. Please ", "restate the inequality to be <=0. The ability to use the old ", "behavior will be removed in a future release.") .hinjac <- match.fun(hinjac) hinjac <- function(x) -.hinjac(x) } } S0 <- nloptr(x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, eval_g_ineq = hin, eval_jac_g_ineq = hinjac, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/finite.diff.R0000644000176200001440000000327014472612401014304 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: finite.diff.R # Author: Jelmer Ypma # Date: 24 July 2011 # # CHANGELOG # # 2023-02-10: Tweaked for efficiency and clarity. Also switched to using vapply # which is both faster and type-safe. Not sure if we need to carry # both this and nl.grad/jacobian but not changing for now. # (Avraham Adler) # # Approximate the gradient of a function using finite differences. # # Input: # func : calculate finite difference approximation for the gradient of # this function # .x : evaluate at this point # indices : calculate finite difference approximation only for .x-indices # in this vector (optional) # stepSize : relative size of the step between x and x + h (optional) # ... : arguments that are passed to the user-defined function (func) # # Output: matrix with finite difference approximations # # http://en.wikipedia.org/wiki/Numerical_differentiation finite.diff <- function(func, .x, indices = seq_along(.x), stepSize = sqrt(.Machine$double.eps), ...) { # if we evaluate at values close to 0, we need a different step size stepSizeVec <- pmax(abs(.x), 1) * stepSize fx <- func(.x, ...) approx.gradf.index <- function(i, .x, func, fx, stepSizeVec, ...) { x_prime <- .x x_prime[i] <- .x[i] + stepSizeVec[i] stepSizeVec[i] <- x_prime[i] - .x[i] fx_prime <- func(x_prime, ...) (fx_prime - fx) / stepSizeVec[i] } vapply(indices, approx.gradf.index, double(length(fx)), .x = .x, func = func, fx = fx, stepSizeVec = stepSizeVec, ...) } nloptr/R/direct.R0000644000176200001440000001322214472715012013371 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: direct.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Direct. # # CHANGELOG # 2023-02-10: Tweaks for efficiency and readability (Avraham Adler) #' DIviding RECTangles Algorithm for Global Optimization #' #' DIRECT is a deterministic search algorithm based on systematic division of #' the search domain into smaller and smaller hyperrectangles. The DIRECT_L #' makes the algorithm more biased towards local search (more efficient for #' functions without too many minima). #' #' The DIRECT and DIRECT-L algorithms start by rescaling the bound constraints #' to a hypercube, which gives all dimensions equal weight in the search #' procedure. If your dimensions do not have equal weight, e.g. if you have a #' ``long and skinny'' search space and your function varies at about the same #' speed in all directions, it may be better to use unscaled variant of the #' DIRECT algorithm. #' #' The algorithms only handle finite bound constraints which must be provided. #' The original versions may include some support for arbitrary nonlinear #' inequality, but this has not been tested. #' #' The original versions do not have randomized or unscaled variants, so these #' options will be disregarded for these versions. #' #' @aliases direct directL #' #' @param fn objective function that is to be minimized. #' @param lower,upper lower and upper bound constraints. #' @param scaled logical; shall the hypercube be scaled before starting. #' @param randomized logical; shall some randomization be used to decide which #' dimension to halve next in the case of near-ties. #' @param original logical; whether to use the original implementation by #' Gablonsky -- the performance is mostly similar. #' @param nl.info logical; shall the original NLopt info been shown. #' @param control list of options, see \code{nl.opts} for help. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export direct #' #' @author Hans W. Borchers #' #' @note The DIRECT_L algorithm should be tried first. #' #' @seealso The \code{dfoptim} package will provide a pure R version of this #' algorithm. #' #' @references D. R. Jones, C. D. Perttunen, and B. E. Stuckmann, #' ``Lipschitzian optimization without the Lipschitz constant,'' J. #' Optimization Theory and Applications, vol. 79, p. 157 (1993). #' #' J. M. Gablonsky and C. T. Kelley, ``A locally-biased form of the DIRECT #' algorithm," J. Global Optimization, vol. 21 (1), p. 27-37 (2001). #' #' @examples #' #' ### Minimize the Hartmann6 function #' hartmann6 <- function(x) { #' a <- c(1.0, 1.2, 3.0, 3.2) #' A <- matrix(c(10.0, 0.05, 3.0, 17.0, #' 3.0, 10.0, 3.5, 8.0, #' 17.0, 17.0, 1.7, 0.05, #' 3.5, 0.1, 10.0, 10.0, #' 1.7, 8.0, 17.0, 0.1, #' 8.0, 14.0, 8.0, 14.0), nrow=4, ncol=6) #' B <- matrix(c(.1312,.2329,.2348,.4047, #' .1696,.4135,.1451,.8828, #' .5569,.8307,.3522,.8732, #' .0124,.3736,.2883,.5743, #' .8283,.1004,.3047,.1091, #' .5886,.9991,.6650,.0381), nrow=4, ncol=6) #' fun <- 0 #' for (i in 1:4) { #' fun <- fun - a[i] * exp(-sum(A[i,] * (x - B[i,]) ^ 2)) #' } #' fun #' } #' S <- directL(hartmann6, rep(0, 6), rep(1, 6), #' nl.info = TRUE, control = list(xtol_rel = 1e-8, maxeval = 1000)) #' ## Number of Iterations....: 1000 #' ## Termination conditions: stopval: -Inf #' ## xtol_rel: 1e-08, maxeval: 1000, ftol_rel: 0, ftol_abs: 0 #' ## Number of inequality constraints: 0 #' ## Number of equality constraints: 0 #' ## Current value of objective function: -3.32236800687327 #' ## Current value of controls: #' ## 0.2016884 0.1500025 0.4768667 0.2753391 0.311648 0.6572931 #' direct <- function(fn, lower, upper, scaled = TRUE, original = FALSE, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) if (scaled) { opts["algorithm"] <- "NLOPT_GN_DIRECT" } else { opts["algorithm"] <- "NLOPT_GN_DIRECT_NOSCAL" } if (original) opts["algorithm"] <- "NLOPT_GN_ORIG_DIRECT" fun <- match.fun(fn) fn <- function(x) fun(x, ...) x0 <- (lower + upper) / 2 S0 <- nloptr(x0, eval_f = fn, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } #' @export directL #' @rdname direct directL <- function(fn, lower, upper, randomized = FALSE, original = FALSE, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) if (randomized) { opts["algorithm"] <- "NLOPT_GN_DIRECT_L_RAND" } else { opts["algorithm"] <- "NLOPT_GN_DIRECT_L" } if (original) opts["algorithm"] <- "NLOPT_GN_ORIG_DIRECT_L" fun <- match.fun(fn) fn <- function(x) fun(x, ...) x0 <- (lower + upper) / 2 S0 <- nloptr(x0, eval_f = fn, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/tnewton.R0000644000176200001440000000700014472612401013610 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: tnewton.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Preconditioned Truncated Newton. # # CHANGELOG # 2023-02-08: Cleanup and tweaks for safety and efficiency (Avraham Adler) # #' Preconditioned Truncated Newton #' #' Truncated Newton methods, also called Newton-iterative methods, solve an #' approximating Newton system using a conjugate-gradient approach and are #' related to limited-memory BFGS. #' #' Truncated Newton methods are based on approximating the objective with a #' quadratic function and applying an iterative scheme such as the linear #' conjugate-gradient algorithm. #' #' @param x0 starting point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param gr gradient of function \code{fn}; will be calculated numerically if #' not specified. #' @param lower,upper lower and upper bound constraints. #' @param precond logical; preset L-BFGS with steepest descent. #' @param restart logical; restarting L-BFGS with steepest descent. #' @param nl.info logical; shall the original NLopt info been shown. #' @param control list of options, see \code{nl.opts} for help. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 1) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export tnewton #' #' @author Hans W. Borchers #' #' @note Less reliable than Newton's method, but can handle very large #' problems. #' #' @seealso \code{\link{lbfgs}} #' #' @references R. S. Dembo and T. Steihaug, ``Truncated Newton algorithms for #' large-scale optimization,'' Math. Programming 26, p. 190-212 (1982). #' #' @examples #' #' flb <- function(x) { #' p <- length(x) #' sum(c(1, rep(4, p - 1)) * (x - c(1, x[-p]) ^ 2) ^ 2) #' } #' # 25-dimensional box constrained: par[24] is *not* at boundary #' S <- tnewton(rep(3, 25L), flb, lower = rep(2, 25L), upper = rep(4, 25L), #' nl.info = TRUE, control = list(xtol_rel = 1e-8)) #' ## Optimal value of objective function: 368.105912874334 #' ## Optimal value of controls: 2 ... 2 2.109093 4 #' tnewton <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, precond = TRUE, restart = TRUE, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) if (precond) { if (restart) opts["algorithm"] <- "NLOPT_LD_TNEWTON_PRECOND_RESTART" else opts["algorithm"] <- "NLOPT_LD_TNEWTON_PRECOND" } else { if (restart) opts["algorithm"] <- "NLOPT_LD_TNEWTON_RESTART" else opts["algorithm"] <- "NLOPT_LD_TNEWTON" } fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (is.null(gr)) { gr <- function(x) nl.grad(x, fn) } else { .gr <- match.fun(gr) gr <- function(x) .gr(x, ...) } S0 <- nloptr(x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/varmetric.R0000644000176200001440000000616714472612401014123 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: varmetric.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Varmetric. # # CHANGELOG # 2023-02-08: Cleanup and tweaks for safety and efficiency (Avraham Adler) # #' Shifted Limited-memory Variable-metric #' #' Shifted limited-memory variable-metric algorithm. #' #' Variable-metric methods are a variant of the quasi-Newton methods, #' especially adapted to large-scale unconstrained (or bound constrained) #' minimization. #' #' @param x0 initial point for searching the optimum. #' @param fn objective function to be minimized. #' @param gr gradient of function \code{fn}; will be calculated numerically if #' not specified. #' @param rank2 logical; if true uses a rank-2 update method, else rank-1. #' @param lower,upper lower and upper bound constraints. #' @param nl.info logical; shall the original NLopt info been shown. #' @param control list of control parameters, see \code{nl.opts} for help. #' @param ... further arguments to be passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export varmetric #' #' @author Hans W. Borchers #' #' @note Based on L. Luksan's Fortran implementation of a shifted #' limited-memory variable-metric algorithm. #' #' @seealso \code{\link{lbfgs}} #' #' @references J. Vlcek and L. Luksan, ``Shifted limited-memory variable metric #' methods for large-scale unconstrained minimization,'' J. Computational Appl. #' Math. 186, p. 365-390 (2006). #' #' @examples #' #' flb <- function(x) { #' p <- length(x) #' sum(c(1, rep(4, p-1)) * (x - c(1, x[-p])^2)^2) #' } #' # 25-dimensional box constrained: par[24] is *not* at the boundary #' S <- varmetric(rep(3, 25), flb, lower=rep(2, 25), upper=rep(4, 25), #' nl.info = TRUE, control = list(xtol_rel=1e-8)) #' ## Optimal value of objective function: 368.105912874334 #' ## Optimal value of controls: 2 ... 2 2.109093 4 #' varmetric <- function(x0, fn, gr = NULL, rank2 = TRUE, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) if (rank2) opts["algorithm"] <- "NLOPT_LD_VAR2" else opts["algorithm"] <- "NLOPT_LD_VAR1" fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (is.null(gr)) { gr <- function(x) nl.grad(x, fn) } else { .gr <- match.fun(gr) gr <- function(x) .gr(x, ...) } S0 <- nloptr(x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/nloptr-package.R0000644000176200001440000001220614613534600015026 0ustar liggesusers#' R interface to NLopt #' #' nloptr is an R interface to NLopt, a free/open-source library for nonlinear #' optimization started by Steven G. Johnson, providing a common interface for #' a number of different free optimization routines available online as well as #' original implementations of various other algorithms. The NLopt library is #' available under the GNU Lesser General Public License (LGPL), and the #' copyrights are owned by a variety of authors. Most of the information here #' has been taken from #' \href{https://nlopt.readthedocs.io/en/latest/}{the NLopt website}, #' where more details are available. #' #' NLopt addresses general nonlinear optimization problems of the form: #' #' \deqn{\min f(x)\quad x\in R^n}{min f(x) x in R^n} #' #' \deqn{\textrm{s.t. }\\ g(x) \leq 0\\ h(x) = 0\\ lb \leq x \leq ub}{ #' s.t. g(x) <= 0 h(x) = 0 lb <= x <= ub} #' #' where \eqn{f(x)} is the objective function to be minimized and \eqn{x} #' represents the \eqn{n} optimization parameters. This problem may optionally #' be subject to the bound constraints (also called box constraints), \eqn{lb} #' and \eqn{ub}. For partially or totally unconstrained problems the bounds can #' take \code{-Inf} or \code{Inf}. One may also optionally have \eqn{m} #' nonlinear inequality constraints (sometimes called a nonlinear programming #' problem), which can be specified in \eqn{g(x)}, and equality constraints that #' can be specified in \eqn{h(x)}. Note that not all of the algorithms in NLopt #' can handle constraints. #' #' An optimization problem can be solved with the general \code{nloptr} #' interface, or using one of the wrapper functions for the separate algorithms; #' \code{auglag}, \code{bobyqa}, \code{ccsaq}, \code{cobyla}, \code{crs2lm}, #' \code{direct}, \code{directL}, \code{isres}, \code{lbfgs}, \code{mlsl}, #' \code{mma}, \code{neldermead}, \code{newuoa}, \code{sbplx}, \code{slsqp}, #' \code{stogo}, \code{tnewton}, \code{varmetric}. #' #' \tabular{ll}{Package: \tab nloptr\cr Type: \tab Package\cr Version: \tab #' 2.0.3\cr Date: \tab 2022-05-26\cr License: \tab L-GPL >= 3\cr} #' #' @name nloptr-package #' #' @useDynLib nloptr, .registration = TRUE #' #' @author Steven G. Johnson and others (C code) \cr Jelmer Ypma (R interface) #' \cr Hans W. Borchers (wrappers) #' #' @note See ?nloptr for more examples. #' #' @seealso \code{\link{optim}} \code{\link{nlm}} \code{\link{nlminb}} #' \code{Rsolnp::Rsolnp} \code{Rsolnp::solnp} \code{\link{nloptr}} #' \code{\link{auglag}} \code{\link{bobyqa}} \code{\link{ccsaq}} #' \code{\link{cobyla}} \code{\link{crs2lm}} \code{\link{direct}} #' \code{\link{directL}} \code{\link{isres}} \code{\link{lbfgs}} #' \code{\link{mlsl}} \code{\link{mma}} \code{\link{neldermead}} #' \code{\link{newuoa}} \code{\link{sbplx}} \code{\link{slsqp}} #' \code{\link{stogo}} \code{\link{tnewton}} \code{\link{varmetric}} #' #' @references Steven G. Johnson, The NLopt nonlinear-optimization package, #' \url{https://nlopt.readthedocs.io/en/latest/} #' #' @keywords optimize interface internal #' #' @examples #' #' # Example problem, number 71 from the Hock-Schittkowsky test suite. #' # #' # \min_{x} x1 * x4 * (x1 + x2 + x3) + x3 #' # s.t. #' # x1 * x2 * x3 * x4 >= 25 #' # x1 ^ 2 + x2 ^ 2 + x3 ^ 2 + x4 ^ 2 = 40 #' # 1 <= x1, x2, x3, x4 <= 5 #' # #' # we re-write the inequality as #' # 25 - x1 * x2 * x3 * x4 <= 0 #' # #' # and the equality as #' # x1 ^ 2 + x2 ^ 2 + x3 ^ 2 + x4 ^ 2 - 40 = 0 #' # #' # x0 = (1, 5, 5, 1) #' # #' # optimal solution = (1.000000, 4.742999, 3.821151, 1.379408) #' #' library('nloptr') #' #' # #' # f(x) = x1 * x4 * (x1 + x2 + x3) + x3 #' # #' eval_f <- function(x) { #' list("objective" = x[1] * x[4] * (x[1] + x[2] + x[3]) + x[3], #' "gradient" = c(x[1] * x[4] + x[4] * (x[1] + x[2] + x[3]), #' x[1] * x[4], #' x[1] * x[4] + 1.0, #' x[1] * (x[1] + x[2] + x[3]))) #' } #' #' # constraint functions #' # inequalities #' eval_g_ineq <- function(x) { #' constr <- c(25 - x[1] * x[2] * x[3] * x[4]) #' #' grad <- c(-x[2] * x[3] * x[4], #' -x[1] * x[3] * x[4], #' -x[1] * x[2] * x[4], #' -x[1] * x[2] * x[3] ) #' list("constraints" = constr, "jacobian" = grad) #' } #' #' # equalities #' eval_g_eq <- function(x) { #' constr <- c(x[1] ^ 2 + x[2] ^ 2 + x[3] ^ 2 + x[4] ^ 2 - 40) #' #' grad <- c(2.0 * x[1], #' 2.0 * x[2], #' 2.0 * x[3], #' 2.0 * x[4]) #' list("constraints" = constr, "jacobian" = grad) #' } #' #' # initial values #' x0 <- c(1, 5, 5, 1) #' #' # lower and upper bounds of control #' lb <- c(1, 1, 1, 1) #' ub <- c(5, 5, 5, 5) #' #' #' local_opts <- list("algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1.0e-7) #' opts <- list("algorithm" = "NLOPT_LD_AUGLAG", #' "xtol_rel" = 1.0e-7, #' "maxeval" = 1000, #' "local_opts" = local_opts) #' #' res <- nloptr(x0 = x0, #' eval_f = eval_f, #' lb = lb, #' ub = ub, #' eval_g_ineq = eval_g_ineq, #' eval_g_eq = eval_g_eq, #' opts = opts) #' print(res) "_PACKAGE" nloptr/R/zzz.R0000644000176200001440000000054114763300100012743 0ustar liggesusers.onLoad <- function(libname, pkgname) { #nocov start # Set the option to TRUE if it has not been set before. if (is.null(getOption("nloptr.show.inequality.warning"))) options("nloptr.show.inequality.warning" = TRUE) } .onUnLoad <- function(libpath) { library.dynam.unload("nloptr", libpath) } #nocov end have.nlopt.ld.lbfgs.nocedal <- FALSE nloptr/R/lbfgs.R0000644000176200001440000000653214472612401013220 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: lbfgs.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Low-storage BFGS. # # CHANGELOG # # 2023-02-09: Cleanup and tweaks for safety and efficiency (Avraham Adler) # #' Low-storage BFGS #' #' Low-storage version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. #' #' The low-storage (or limited-memory) algorithm is a member of the class of #' quasi-Newton optimization methods. It is well suited for optimization #' problems with a large number of variables. #' #' One parameter of this algorithm is the number \code{m} of gradients to #' remember from previous optimization steps. NLopt sets \code{m} to a #' heuristic value by default. It can be changed by the NLopt function #' \code{set_vector_storage}. #' #' @param x0 initial point for searching the optimum. #' @param fn objective function to be minimized. #' @param gr gradient of function \code{fn}; will be calculated numerically if #' not specified. #' @param lower,upper lower and upper bound constraints. #' @param nl.info logical; shall the original NLopt info been shown. #' @param control list of control parameters, see \code{nl.opts} for help. #' @param ... further arguments to be passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export lbfgs #' #' @author Hans W. Borchers #' #' @note Based on a Fortran implementation of the low-storage BFGS algorithm #' written by L. Luksan, and posted under the GNU LGPL license. #' #' @seealso \code{\link{optim}} #' #' @references J. Nocedal, ``Updating quasi-Newton matrices with limited #' storage,'' Math. Comput. 35, 773-782 (1980). #' #' D. C. Liu and J. Nocedal, ``On the limited memory BFGS method for large #' scale optimization,'' Math. Programming 45, p. 503-528 (1989). #' #' @examples #' #' flb <- function(x) { #' p <- length(x) #' sum(c(1, rep(4, p-1)) * (x - c(1, x[-p])^2)^2) #' } #' # 25-dimensional box constrained: par[24] is *not* at the boundary #' S <- lbfgs(rep(3, 25), flb, lower=rep(2, 25), upper=rep(4, 25), #' nl.info = TRUE, control = list(xtol_rel=1e-8)) #' ## Optimal value of objective function: 368.105912874334 #' ## Optimal value of controls: 2 ... 2 2.109093 4 #' lbfgs <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LD_LBFGS" fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (is.null(gr)) { gr <- function(x) nl.grad(x, fn) } else { .gr <- match.fun(gr) gr <- function(x) .gr(x, ...) } S0 <- nloptr(x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/nloptr.get.default.options.R0000644000176200001440000003515014763300100017323 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: nloptr.default.options.R # Author: Jelmer Ypma # Date: 7 August 2011 # # Defines a data.frame with fields: # name: name of the option. # type: type (numeric, logical, integer, character). # possible_values: string explaining the values the option can take. # default: default value of the option (as a string). # is_termination_condition: is this option part of the termination conditions? # description: description of the option (taken from NLopt website # if it's an option that is passed on to NLopt). # # CHANGELOG: # 2014-07-12: Changed from creating a data.frame to a function returning a # data.frame. # 2023-02-09: Cleanup and tweaks for safety and efficiency (AA) #' Return a data.frame with all the options that can be supplied to nloptr. #' #' This function returns a data.frame with all the options that can be supplied #' to \code{\link[nloptr:nloptr]{nloptr}}. The data.frame contains the default #' values of the options and an explanation. A user-friendly way to show these #' options is by using the function #' \code{\link[nloptr:nloptr.print.options]{nloptr.print.options}}. #' #' @return The return value contains a \code{data.frame} with the following #' elements #' \item{name}{name of the option} #' \item{type}{type (numeric, logical, integer, character)} #' \item{possible_values}{string explaining the values the option can take} #' \item{default}{default value of the option (as a string)} #' \item{is_termination_condition}{is this option part of the termination #' conditions?} #' \item{description}{description of the option (taken from NLopt website #' if it's an option that is passed on to NLopt).} #' #' @export nloptr.get.default.options #' #' @author Jelmer Ypma #' #' @seealso #' \code{\link[nloptr:nloptr]{nloptr}} #' \code{\link[nloptr:nloptr.print.options]{nloptr.print.options}} #' #' @keywords optimize interface #' nloptr.get.default.options <- function() { dat.opts <- data.frame( rbind( c("algorithm", "character", paste(c("NLOPT_GN_DIRECT", "NLOPT_GN_DIRECT_L", "NLOPT_GN_DIRECT_L_RAND", "NLOPT_GN_DIRECT_NOSCAL", "NLOPT_GN_DIRECT_L_NOSCAL", "NLOPT_GN_DIRECT_L_RAND_NOSCAL", "NLOPT_GN_ORIG_DIRECT", "NLOPT_GN_ORIG_DIRECT_L", "NLOPT_GD_STOGO", "NLOPT_GD_STOGO_RAND", "NLOPT_LD_SLSQP", if (have.nlopt.ld.lbfgs.nocedal) "NLOPT_LD_LBFGS_NOCEDAL", "NLOPT_LD_LBFGS", "NLOPT_LN_PRAXIS", "NLOPT_LD_VAR1", "NLOPT_LD_VAR2", "NLOPT_LD_TNEWTON", "NLOPT_LD_TNEWTON_RESTART", "NLOPT_LD_TNEWTON_PRECOND", "NLOPT_LD_TNEWTON_PRECOND_RESTART", "NLOPT_GN_CRS2_LM", "NLOPT_GN_MLSL", "NLOPT_GD_MLSL", "NLOPT_GN_MLSL_LDS", "NLOPT_GD_MLSL_LDS", "NLOPT_LD_MMA", "NLOPT_LD_CCSAQ", "NLOPT_LN_COBYLA", "NLOPT_LN_NEWUOA", "NLOPT_LN_NEWUOA_BOUND", "NLOPT_LN_NELDERMEAD", "NLOPT_LN_SBPLX", "NLOPT_LN_AUGLAG", "NLOPT_LD_AUGLAG", "NLOPT_LN_AUGLAG_EQ", "NLOPT_LD_AUGLAG_EQ", "NLOPT_LN_BOBYQA", "NLOPT_GN_ISRES"), collapse = ", "), "none", FALSE, paste("This option is required. Check the NLopt website", "for a description of the algorithms.")), c("stopval", "numeric", "-Inf <= stopval <= Inf", "-Inf", TRUE, paste("Stop minimization when an objective value <= stopval", "is found. Setting stopval to -Inf disables this", "stopping criterion (default).")), c("ftol_rel", "numeric", "ftol_rel > 0", "0.0", TRUE, paste("Stop when an optimization step (or an estimate of", "the optimum) changes the objective function value by", "less than ftol_rel multiplied by the absolute value", "of the function value. If there is any chance that", "your optimum function value is close to zero, you", "might want to set an absolute tolerance with", "ftol_abs as well. Criterion is disabled if ftol_rel", "is non-positive (default).")), c("ftol_abs", "numeric", "ftol_abs > 0", "0.0", TRUE, paste("Stop when an optimization step (or an estimate of", "the optimum) changes the function value by less than", "ftol_abs. Criterion is disabled if ftol_abs is", "non-positive (default).")), c("xtol_rel", "numeric", "xtol_rel > 0", "1.0e-04", TRUE, paste("Stop when an optimization step (or an estimate of", "the optimum) changes every parameter by less than", "xtol_rel multiplied by the absolute value of the", "parameter. If there is any chance that an optimal", "parameter is close to zero, you might want to set an", "absolute tolerance with xtol_abs as well. Criterion", "is disabled if xtol_rel is non-positive.")), c("xtol_abs", "numeric", "xtol_abs > 0", "rep(0.0, length(x0))", TRUE, paste("xtol_abs is a vector of length n (the number of", "elements in x) giving the tolerances: stop when an", "optimization step (or an estimate of the optimum)", "changes every parameter x[i] by less than", "xtol_abs[i]. Criterion is disabled if all elements", "of xtol_abs are non-positive (default).")), c("maxeval", "integer", "maxeval is a positive integer", "100", TRUE, paste("Stop when the number of function evaluations exceeds", "maxeval. This is not a strict maximum: the number of", "function evaluations may exceed maxeval slightly,", "depending upon the algorithm. Criterion is disabled", "if maxeval is non-positive.")), c("maxtime", "numeric", "maxtime > 0", "-1.0", TRUE, paste("Stop when the optimization time (in seconds) exceeds", "maxtime. This is not a strict maximum: the time may", "exceed maxtime slightly, depending upon the", "algorithm and on how slow your function evaluation", "is. Criterion is disabled if maxtime is non-positive", "(default).")), c("tol_constraints_ineq", "numeric", "tol_constraints_ineq > 0.0", "rep(1e-8, num_constraints_ineq)", FALSE, paste("The parameter tol_constraints_ineq is a vector of", "tolerances. Each tolerance corresponds to one of the", "inequality constraints. The tolerance is used for", "the purpose of stopping criteria only: a point x is", "considered feasible for judging whether to stop the", "optimization if eval_g_ineq(x) <= tol. A tolerance", "of zero means that NLopt will try not to consider", "any x to be converged unless eval_g_ineq(x) is", "strictly non-positive; generally, at least a small", "positive tolerance is advisable to reduce", "sensitivity to rounding errors. By default the", "tolerances for all inequality constraints are set to", "1e-8.")), c("tol_constraints_eq", "numeric", "tol_constraints_eq > 0.0", "rep(1e-8, num_constraints_eq)", FALSE, paste("The parameter tol_constraints_eq is a vector of", "tolerances. Each tolerance corresponds to one of the", "equality constraints. The tolerance is used for the", "purpose of stopping criteria only: a point x is", "considered feasible for judging whether to stop the", "optimization if abs(eval_g_ineq(x)) <= tol. For", "equality constraints, a small positive tolerance is", "strongly advised in order to allow NLopt to converge", "even if the equality constraint is slightly nonzero.", "By default the tolerances for all quality", "constraints are set to 1e-8.")), c("print_level", "integer", "0, 1, 2, or 3", "0", FALSE, paste("The option print_level controls how much output is", "shown during the optimization process. Possible", "values: 0 (default): no output; 1: show iteration", "number and value of objective function; 2: 1 + show", "value of (in)equalities; 3: 2 + show value of", "controls.")), c("check_derivatives", "logical", "TRUE or FALSE", "FALSE", FALSE, paste("The option check_derivatives can be activated to", "compare the user-supplied analytic gradients with", "finite difference approximations.")), c("check_derivatives_tol", "numeric", "check_derivatives_tol > 0.0", "1e-04", FALSE, paste("The option check_derivatives_tol determines when a", "difference between an analytic gradient and its", "finite difference approximation is flagged as an", "error.")), c("check_derivatives_print", "character", "'none', 'all', 'errors',", "all", FALSE, paste("The option check_derivatives_print controls the", "output of the derivative checker (if", "check_derivatives == TRUE). All comparisons are", "shown ('all'), only those comparisions that resulted", "in an error ('error'), or only the number of errors", "is shown ('none').")), c("print_options_doc", "logical", "TRUE or FALSE", "FALSE", FALSE, paste("If TRUE, a description of all options and their", "current and default values is printed to the screen.") ), c("population", "integer", "population is a positive integer", "0", FALSE, paste("Several of the stochastic search algorithms (e.g.,", "CRS, MLSL, and ISRES) start by generating some", "initial population of random points x. By default,", "this initial population size is chosen heuristically", "in some algorithm-specific way, but the initial", "population can by changed by setting a positive", "integer value for population. A population of zero", "implies that the heuristic default will be used.")), c("vector_storage", "integer", "vector_storage is a positive integer", "20", FALSE, paste("Number of gradients to remember from previous", "optimization steps.")), c("ranseed", "integer", "ranseed is a positive integer", "0", FALSE, paste("For stochastic optimization algorithms, pseudorandom", "numbers are generated. Set the random seed using", "ranseed if you want to use a 'deterministic'", "sequence of pseudorandom numbers, i.e. the same", "sequence from run to run. If ranseed is 0 (default),", "the seed for the random numbers is generated from", "the system time, so that you will get a different", "sequence of pseudorandom numbers each time you run", "your program.")) ), stringsAsFactors = FALSE) names(dat.opts) <- c("name", "type", "possible_values", "default", "is_termination_condition", "description") dat.opts } nloptr/R/print.nloptr.R0000644000176200001440000000642614472612401014576 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: print.nloptr.R # Author: Jelmer Ypma # Date: 10 June 2010 # # This function prints some basic output of a nloptr # ojbect. The information is only available after it # has been solved. # # show.controls is TRUE, FALSE or a vector of indices. # Use this option to show none, or only a subset of # the controls. # # 2011-01-13: added show.controls option # 2011-08-07: show 'optimal value' instead of 'current value' # if status == 1, 2, 3, or 4 # 2023-02-09: Cleanup and tweaks for safety and efficiency (Avraham Adler) #' Print results after running nloptr #' #' This function prints the nloptr object that holds the results from a #' minimization using \code{nloptr}. #' #' @param x object containing result from minimization. #' @param show.controls Logical or vector with indices. Should we show the value #' of the control variables in the solution? If \code{show.controls} is a #' vector with indices, it is used to select which control variables should be #' shown. This can be useful if the model contains a set of parameters of #' interest and a set of nuisance parameters that are not of immediate #' interest. #' @param ... further arguments passed to or from other methods. #' #' @method print nloptr #' @export #' #' @author Jelmer Ypma #' #' @seealso \code{\link[nloptr:nloptr]{nloptr}} #' #' @keywords optimize interface #' print.nloptr <- function(x, show.controls = TRUE, ...) { cat("\nCall:\n", deparse(x$call), "\n\n", sep = "", fill = TRUE) cat(paste("Minimization using NLopt version", x$version, "\n"), fill = TRUE) cat(unlist(strsplit(paste("NLopt solver status:", x$status, "(", x$message, ")\n"), " ", fixed = TRUE)), fill = TRUE) cat(paste("Number of Iterations....:", x$iterations, "\n")) cat(paste("Termination conditions: ", x$termination_conditions, "\n")) cat(paste("Number of inequality constraints: ", x$num_constraints_ineq, "\n")) cat(paste("Number of equality constraints: ", x$num_constraints_eq, "\n")) # if show.controls is TRUE or FALSE, show all or none of the controls if (is.logical(show.controls) && show.controls) { controls.indices <- seq_along(x$solution) } # if show.controls is a vector with indices, rename this vector # and define show.controls as TRUE if (is.numeric(show.controls)) { controls.indices <- show.controls show.controls <- TRUE } # if solved successfully if (x$status >= 1 && x$status <= 4) { cat(paste("Optimal value of objective function: ", x$objective, "\n")) if (show.controls) { if (length(controls.indices) < length(x$solution)) { cat("Optimal value of user-defined subset of controls: ") } else { cat("Optimal value of controls: ") } cat(x$solution[controls.indices], fill = TRUE) cat("\n") } } else { cat(paste("Current value of objective function: ", x$objective, "\n")) if (show.controls) { if (length(controls.indices) < length(x$solution)) { cat("Current value of user-defined subset of controls: ") } else { cat("Current value of controls: ") } cat(x$solution[controls.indices], fill = TRUE) cat("\n") } } cat("\n") } nloptr/R/mma.R0000644000176200001440000001434314634272373012706 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: mma.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using MMA. # # CHANGELOG # # 2023-02-09: Cleanup and tweaks for safety and efficiency. (Avraham Adler) # 2024-06-04: Switched desired direction of the hin/hinjac inequalities, leaving # the old behavior as the default for now. Also cleaned up the HS100 # example. (Avraham Adler) # #' Method of Moving Asymptotes #' #' Globally-convergent method-of-moving-asymptotes (\acronym{MMA}) algorithm for #' gradient-based local optimization, including nonlinear inequality #' constraints (but not equality constraints). #' #' This is an improved \acronym{CCSA} ("conservative convex separable #' approximation") variant of the original \acronym{MMA} algorithm published by #' Svanberg in 1987, which has become popular for topology optimization. #' #' @param x0 starting point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param gr gradient of function \code{fn}; will be calculated numerically if #' not specified. #' @param lower,upper lower and upper bound constraints. #' @param hin function defining the inequality constraints, that is #' \code{hin <= 0} for all components. #' @param hinjac Jacobian of function \code{hin}; will be calculated #' numerically if not specified. #' @param nl.info logical; shall the original NLopt info been shown. #' @param control list of options, see \code{nl.opts} for help. #' @param deprecatedBehavior logical; if \code{TRUE} (default for now), the old #' behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} #' instead of \eqn{\le 0}. This will be reversed in a future release and #' eventually removed. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 1) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export mma #' #' @author Hans W. Borchers #' #' @note \dQuote{Globally convergent} does not mean that this algorithm #' converges to the global optimum; rather, it means that the algorithm is #' guaranteed to converge to some local minimum from any feasible starting #' point. #' #' @seealso \code{\link{slsqp}} #' #' @references Krister Svanberg, \dQuote{A class of globally convergent #' optimization methods based on conservative convex separable #' approximations}, SIAM J. Optim. 12 (2), p. 555-573 (2002). #' #' @examples #' #' # Solve the Hock-Schittkowski problem no. 100 with analytic gradients #' # See https://apmonitor.com/wiki/uploads/Apps/hs100.apm #' #' x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) #' fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + #' 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + #' x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} #' #' hin.hs100 <- function(x) {c( #' 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, #' 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, #' 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, #' 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - #' 11 * x[7]) #' } #' #' gr.hs100 <- function(x) { #' c( 2 * x[1] - 20, #' 10 * x[2] - 120, #' 4 * x[3] ^ 3, #' 6 * x[4] - 66, #' 60 * x[5] ^ 5, #' 14 * x[6] - 4 * x[7] - 10, #' 4 * x[7] ^ 3 - 4 * x[6] - 8) #' } #' #' hinjac.hs100 <- function(x) { #' matrix(c(4 * x[1], 12 * x[2] ^ 3, 1, 8 * x[4], 5, 0, 0, #' 7, 3, 20 * x[3], 1, -1, 0, 0, #' 23, 2 * x[2], 0, 0, 0, 12 * x[6], -8, #' 8 * x[1] - 3 * x[2], 2 * x[2] - 3 * x[1], 4 * x[3], 0, 0, 5, -11), #' nrow = 4, byrow = TRUE) #' } #' #' # The optimum value of the objective function should be 680.6300573 #' # A suitable parameter vector is roughly #' # (2.330, 1.9514, -0.4775, 4.3657, -0.6245, 1.0381, 1.5942) #' #' # Using analytic Jacobian #' S <- mma(x0.hs100, fn.hs100, gr = gr.hs100, #' hin = hin.hs100, hinjac = hinjac.hs100, #' nl.info = TRUE, control = list(xtol_rel = 1e-8), #' deprecatedBehavior = FALSE) #' #' # Using computed Jacobian #' S <- mma(x0.hs100, fn.hs100, hin = hin.hs100, #' nl.info = TRUE, control = list(xtol_rel = 1e-8), #' deprecatedBehavior = FALSE) #' mma <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, nl.info = FALSE, control = list(), deprecatedBehavior = TRUE, ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LD_MMA" fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (is.null(gr)) { gr <- function(x) nl.grad(x, fn) } else { .gr <- match.fun(gr) gr <- function(x) .gr(x, ...) } if (!is.null(hin)) { if (deprecatedBehavior) { warning("The old behavior for hin >= 0 has been deprecated. Please ", "restate the inequality to be <=0. The ability to use the old ", "behavior will be removed in a future release.") .hin <- match.fun(hin) hin <- function(x) -.hin(x, ...) # change hin >= 0 to hin <= 0 ! } if (is.null(hinjac)) { hinjac <- function(x) nl.jacobian(x, hin) } else if (deprecatedBehavior) { warning("The old behavior for hinjac >= 0 has been deprecated. Please ", "restate the inequality to be <=0. The ability to use the old ", "behavior will be removed in a future release.") .hinjac <- match.fun(hinjac) hinjac <- function(x) -.hinjac(x) } } S0 <- nloptr(x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, eval_g_ineq = hin, eval_jac_g_ineq = hinjac, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/nloptr.print.options.R0000644000176200001440000000556214472612401016270 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: nloptr.print.options.R # Author: Jelmer Ypma # Date: 8 August 2011 # # Print list of all options with description. # # Input: # opts.show: the description of the options in this list are shown # (optional, default is to show all options) # opts.user: list with user defined options (optional) # Output: options, default values, user values if supplied) # and description printed to screen. No return value. # # 2011-08-08: Added opts.show argument to only show a subset of all options. # 2023-02-09: Cleanup and tweaks for safety and efficiency (Avraham Adler) #' Print description of nloptr options #' #' This function prints a list of all the options that can be set when solving #' a minimization problem using \code{nloptr}. #' #' @param opts.show list or vector with names of options. A description will be #' shown for the options in this list. By default, a description of all #' options is shown. #' @param opts.user object containing user supplied options. This argument is #' optional. It is used when \code{nloptr.print.options} is called from #' \code{nloptr}. In that case options are listed if \code{print_options_doc} #' is set to \code{TRUE} when passing a minimization problem to \code{nloptr}. #' #' @export nloptr.print.options #' #' @author Jelmer Ypma #' #' @seealso \code{\link[nloptr:nloptr]{nloptr}} #' #' @keywords optimize interface #' #' @examples #' #' library('nloptr') #' nloptr.print.options() #' #' nloptr.print.options(opts.show = c("algorithm", "check_derivatives")) #' #' opts <- list("algorithm"="NLOPT_LD_LBFGS", #' "xtol_rel"=1.0e-8) #' nloptr.print.options(opts.user = opts) #' nloptr.print.options <- function(opts.show = NULL, opts.user = NULL) { # Default is to show all options if no list of options is supplied nloptr.show.options <- nloptr.get.default.options() if (!is.null(opts.show)) { nloptr.show.options <- subset(nloptr.show.options, nloptr.show.options$name %in% opts.show) } # loop over all options and print values for (row.cnt in seq_len(nrow(nloptr.show.options))) { opt <- nloptr.show.options[row.cnt, ] value.current <- ifelse(is.null(opts.user[[opt$name]]), "(default)", opts.user[[opt$name]]) cat(opt$name, "\n", sep = "") cat("\tpossible values: ", paste(strwrap(opt$possible_values, width = 50), collapse = "\n\t "), "\n", sep = "") cat("\tdefault value: ", opt$default, "\n", sep = "") if (!is.null(opts.user)) { cat("\tcurrent value: ", value.current, "\n", sep = "") } cat("\n\t", paste(strwrap(opt$description, width = 70), collapse = "\n\t"), "\n", sep = "") cat("\n") } } nloptr/R/nloptr.R0000644000176200001440000005317014765233776013464 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: nloptr.R # Author: Jelmer Ypma # Date: 9 June 2010 # # Input: # x0 : vector with initial values # eval_f : function to evaluate objective function # (and optionally its gradient) # eval_grad_f : function evaluate the gradient of the objective function # (optional) # lb : lower bounds of the control (optional) # ub : upper bounds of the control (optional) # eval_g_ineq : function to evaluate (non-)linear inequality constraints # that should hold in the solution and its Jacobian # (optional) # eval_jac_g_ineq : function to evaluate Jacobian of the (non-)linear # inequality constraints (optional) # eval_g_eq : function to evaluate (non-)linear equality constraints that # should hold in the solution and its Jacobian (optional) # eval_jac_g_eq : function to evaluate Jacobian of the (non-)linear # equality constraints (optional) # opts : list with options that are passed to nlopt # ... : arguments that are passed to user-defined functions # # Output: structure with inputs and # call : the call that was made to solve # status : integer value with the status of the optimization # (0 is success) # message : more informative message with the status of the optimization # iterations : number of iterations that were executed # objective : value if the objective function in the solution # solution : optimal value of the controls # # CHANGELOG: # 2011-01-13: added print_level option # 2011-07-24: added finite difference gradient checker # 2011-08-07: moved addition of default options to separate function # show documentation of options if print_options_doc == TRUE # 2014-05-05: Replaced cat by message, so messages can now be suppressed by # suppressMessages. # 2015-03-22: Added while-loop around solve statement. This should solve the # problem that NLopt sometimes exits with NLOPT_MAXTIME_REACHED # when no maxtime was set in the options. # 2023-02-08: Removed unneeded or inefficient calls, updated code # stylistically, updated help by using LaTeX and code # decorations. (AA) # #' R interface to NLopt #' #' nloptr is an R interface to NLopt, a free/open-source library for nonlinear #' optimization started by Steven G. Johnson, providing a common interface for a #' number of different free optimization routines available online as well as #' original implementations of various other algorithms. The NLopt library is #' available under the GNU Lesser General Public License (LGPL), and the #' copyrights are owned by a variety of authors. Most of the information here #' has been taken from #' \href{https://nlopt.readthedocs.io/en/latest/}{the NLopt website}, where #' more details are available. #' #' NLopt addresses general nonlinear optimization problems of the form: #' #' \deqn{\min f(x)\quad x\in R^n}{min f(x) x in R^n} #' #' \deqn{\textrm{s.t. }\\ g(x) \leq 0\\ h(x) = 0\\ lb \leq x \leq ub}{ #' s.t. g(x) <= 0 h(x) = 0 lb <= x <= ub} #' #' where \eqn{f(x)} is the objective function to be minimized and \eqn{x} #' represents the \eqn{n} optimization parameters. This problem may optionally #' be subject to the bound constraints (also called box constraints), \eqn{lb} #' and \eqn{ub}. For partially or totally unconstrained problems the bounds can #' take \code{-Inf} or \code{Inf}. One may also optionally have \eqn{m} #' nonlinear inequality constraints (sometimes called a nonlinear programming #' problem), which can be specified in \eqn{g(x)}, and equality constraints that #' can be specified in \eqn{h(x)}. Note that not all of the algorithms in NLopt #' can handle constraints. #' #' @param x0 vector with starting values for the optimization. #' @param eval_f function that returns the value of the objective function. It #' can also return gradient information at the same time in a list with #' elements "objective" and "gradient" (see below for an example). #' @param eval_grad_f function that returns the value of the gradient of the #' objective function. Not all of the algorithms require a gradient. #' @param lb vector with lower bounds of the controls (use \code{-Inf} for #' controls without lower bound), by default there are no lower bounds for any #' of the controls. #' @param ub vector with upper bounds of the controls (use \code{Inf} for #' controls without upper bound), by default there are no upper bounds for any #' of the controls. #' @param eval_g_ineq function to evaluate (non-)linear inequality constraints #' that should hold in the solution. It can also return gradient information #' at the same time in a list with elements "constraints" and "jacobian" (see #' below for an example). #' @param eval_jac_g_ineq function to evaluate the Jacobian of the (non-)linear #' inequality constraints that should hold in the solution. #' @param eval_g_eq function to evaluate (non-)linear equality constraints that #' should hold in the solution. It can also return gradient information at #' the same time in a list with elements "constraints" and "jacobian" (see #' below for an example). #' @param eval_jac_g_eq function to evaluate the Jacobian of the (non-)linear #' equality constraints that should hold in the solution. #' @param opts list with options. The option "\code{algorithm}" is required. #' Check the #' \href{https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/}{NLopt #' website} for a full list of available algorithms. Other options control the #' termination conditions (\code{minf_max, ftol_rel, ftol_abs, xtol_rel,} #' \code{xtol_abs, maxeval, maxtime}). Default is \code{xtol_rel} = 1e-4. More #' information #' \href{https://nlopt.readthedocs.io/en/latest/NLopt_Introduction/#termination-conditions}{here}. #nolint #' A full description of all options is shown by the function #' \code{nloptr.print.options()}. #' #' Some algorithms with equality constraints require the option #' \code{local_opts}, which contains a list with an algorithm and a termination #' condition for the local algorithm. See \code{?`nloptr-package`} for an #' example. #' #' The option \code{print_level} controls how much output is shown during the #' optimization process. Possible values: \tabular{ll}{0 (default) \tab no #' output \cr 1 \tab show iteration number and value of objective function \cr #' 2 \tab 1 + show value of (in)equalities \cr 3 \tab 2 + show value of #' controls} #' #' The option \code{check_derivatives} (default = \code{FALSE}) can be used to #' run to compare the analytic gradients with finite difference approximations. #' The option \code{check_derivatives_print} (\code{'all'} (default), #' \code{'errors'}, \code{'none'}) controls the output of the derivative #' checker, if it is run, showing all comparisons, only those that resulted in #' an error, or none. The option \code{check_derivatives_tol} (default = #' 1e-04), determines when a difference between an analytic gradient and its #' finite difference approximation is flagged as an error. #' #' @param ... arguments that will be passed to the user-defined objective and #' constraints functions. #' #' @return The return value contains a list with the inputs, and additional #' elements #' \item{call}{the call that was made to solve} #' \item{status}{integer value with the status of the optimization (0 is #' success)} #' \item{message}{more informative message with the status of the optimization} #' \item{iterations}{number of iterations that were executed} #' \item{objective}{value if the objective function in the solution} #' \item{solution}{optimal value of the controls} #' \item{version}{version of NLopt that was used} #' #' @export nloptr #' #' @author Steven G. Johnson and others (C code) \cr Jelmer Ypma (R interface) #' #' @note See \code{?`nloptr-package`} for an extended example. #' #' @seealso #' \code{\link[nloptr:nloptr.print.options]{nloptr.print.options}} #' \code{\link[nloptr:check.derivatives]{check.derivatives}} #' \code{\link{optim}} #' \code{\link{nlm}} #' \code{\link{nlminb}} #' \code{Rsolnp::Rsolnp} #' \code{Rsolnp::solnp} #' #' @references Steven G. Johnson, The NLopt nonlinear-optimization package, #' \url{https://github.com/stevengj/nlopt} #' #' @keywords optimize interface #' #' @examples #' #' library('nloptr') #' #' ## Rosenbrock Banana function and gradient in separate functions #' eval_f <- function(x) { #' return(100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2) #'} #' #' eval_grad_f <- function(x) { #' return(c(-400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), #' 200 * (x[2] - x[1] * x[1]))) #'} #' #' #' # initial values #' x0 <- c(-1.2, 1) #' #' opts <- list("algorithm"="NLOPT_LD_LBFGS", #' "xtol_rel"=1.0e-8) #' #' # solve Rosenbrock Banana function #' res <- nloptr(x0=x0, #' eval_f=eval_f, #' eval_grad_f=eval_grad_f, #' opts=opts) #' print(res) #' #' #' ## Rosenbrock Banana function and gradient in one function #' # this can be used to economize on calculations #' eval_f_list <- function(x) { #' return( #' list( #' "objective" = 100 * (x[2] - x[1] * x[1]) ^ 2 + (1 - x[1]) ^ 2, #' "gradient" = c(-400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), #' 200 * (x[2] - x[1] * x[1])))) #'} #' #' # solve Rosenbrock Banana function using an objective function that #' # returns a list with the objective value and its gradient #' res <- nloptr(x0=x0, #' eval_f=eval_f_list, #' opts=opts) #' print(res) #' #' #' #' # Example showing how to solve the problem from the NLopt tutorial. #' # #' # min sqrt(x2) #' # s.t. x2 >= 0 #' # x2 >= (a1*x1 + b1)^3 #' # x2 >= (a2*x1 + b2)^3 #' # where #' # a1 = 2, b1 = 0, a2 = -1, b2 = 1 #' # #' # re-formulate constraints to be of form g(x) <= 0 #' # (a1*x1 + b1)^3 - x2 <= 0 #' # (a2*x1 + b2)^3 - x2 <= 0 #' #' library('nloptr') #' #' #' # objective function #' eval_f0 <- function(x, a, b) { #' return(sqrt(x[2])) #'} #' #' # constraint function #' eval_g0 <- function(x, a, b) { #' return((a*x[1] + b)^3 - x[2]) #'} #' #' # gradient of objective function #' eval_grad_f0 <- function(x, a, b) { #' return(c(0, .5/sqrt(x[2]))) #'} #' #' # Jacobian of constraint #' eval_jac_g0 <- function(x, a, b) { #' return(rbind(c(3*a[1]*(a[1]*x[1] + b[1])^2, -1.0), #' c(3*a[2]*(a[2]*x[1] + b[2])^2, -1.0))) #'} #' #' #' # functions with gradients in objective and constraint function #' # this can be useful if the same calculations are needed for #' # the function value and the gradient #' eval_f1 <- function(x, a, b) { #' return(list("objective"=sqrt(x[2]), #' "gradient"=c(0,.5/sqrt(x[2])))) #'} #' #' eval_g1 <- function(x, a, b) { #' return(list("constraints"=(a*x[1] + b)^3 - x[2], #' "jacobian"=rbind(c(3*a[1]*(a[1]*x[1] + b[1])^2, -1.0), #' c(3*a[2]*(a[2]*x[1] + b[2])^2, -1.0)))) #'} #' #' #' # define parameters #' a <- c(2,-1) #' b <- c(0, 1) #' #' # Solve using NLOPT_LD_MMA with gradient information supplied in separate #' # function. #' res0 <- nloptr(x0=c(1.234,5.678), #' eval_f=eval_f0, #' eval_grad_f=eval_grad_f0, #' lb = c(-Inf,0), #' ub = c(Inf,Inf), #' eval_g_ineq = eval_g0, #' eval_jac_g_ineq = eval_jac_g0, #' opts = list("algorithm"="NLOPT_LD_MMA"), #' a = a, #' b = b) #' print(res0) #' #' # Solve using NLOPT_LN_COBYLA without gradient information #' res1 <- nloptr(x0=c(1.234,5.678), #' eval_f=eval_f0, #' lb = c(-Inf, 0), #' ub = c(Inf, Inf), #' eval_g_ineq = eval_g0, #' opts = list("algorithm" = "NLOPT_LN_COBYLA"), #' a = a, #' b = b) #' print(res1) #' #' #' # Solve using NLOPT_LD_MMA with gradient information in objective function #' res2 <- nloptr(x0=c(1.234, 5.678), #' eval_f=eval_f1, #' lb = c(-Inf, 0), #' ub = c(Inf, Inf), #' eval_g_ineq = eval_g1, #' opts = list("algorithm"="NLOPT_LD_MMA", #' "check_derivatives" = TRUE), #' a = a, #' b = b) #' print(res2) #' nloptr <- function(x0, eval_f, eval_grad_f = NULL, lb = NULL, ub = NULL, eval_g_ineq = NULL, eval_jac_g_ineq = NULL, eval_g_eq = NULL, eval_jac_g_eq = NULL, opts = list(), ...) { # check x0 if (!is.numeric(x0)) stop("x0 must be numeric\n") if (length(x0) == 0) stop("x0 must have length > 0\n") # internal function to check the arguments of the functions .checkfunargs <- function(fun, arglist, funname) { if (!is.function(fun)) stop(funname, " must be a function\n") flist <- formals(fun) if (length(flist) > 1) { fnms <- names(flist)[2:length(flist)] # remove first argument (x) rnms <- names(arglist) m1 <- match(fnms, rnms) if (anyNA(m1)) { mx1 <- which(is.na(m1)) for (i in seq_along(mx1)) { stop(funname, " requires argument '", fnms[mx1[i]], "' but this has not been passed to the 'nloptr' function.\n") } } m2 <- match(rnms, fnms) if (anyNA(m2)) { mx2 <- which(is.na(m2)) for (i in seq_along(mx2)) { stop(rnms[mx2[i]], "' passed to (...) in 'nloptr' but this is not ", "required in the ", funname, " function.\n") } } } } # extract list of additional arguments and check user-defined functions arglist <- list(...) .checkfunargs(eval_f, arglist, "eval_f") if (!is.null(eval_grad_f)) { .checkfunargs(eval_grad_f, arglist, "eval_grad_f") } if (!is.null(eval_g_ineq)) { .checkfunargs(eval_g_ineq, arglist, "eval_g_ineq") } if (!is.null(eval_jac_g_ineq)) { .checkfunargs(eval_jac_g_ineq, arglist, "eval_jac_g_ineq") } if (!is.null(eval_g_eq)) .checkfunargs(eval_g_eq, arglist, "eval_g_eq") if (!is.null(eval_jac_g_eq)) { .checkfunargs(eval_jac_g_eq, arglist, "eval_jac_g_eq") } # define 'infinite' lower and upper bounds of the control if they haven't been # set if (is.null(lb)) {lb <- rep(-Inf, length(x0))} if (is.null(ub)) {ub <- rep(Inf, length(x0))} # if eval_f does not return a list, write a wrapper function combining # eval_f and eval_grad_f if (is.list(eval_f(x0, ...)) || is.null(eval_grad_f)) { eval_f_wrapper <- function(x) {eval_f(x, ...)} } else { eval_f_wrapper <- function(x) { list("objective" = eval_f(x, ...), "gradient" = eval_grad_f(x, ...)) } } # change the environment of the inequality constraint functions that we're # calling num_constraints_ineq <- 0 if (!is.null(eval_g_ineq)) { # if eval_g_ineq does not return a list, write a wrapper function # combining eval_g_ineq and eval_jac_g_ineq if (is.list(eval_g_ineq(x0, ...)) || is.null(eval_jac_g_ineq)) { eval_g_ineq_wrapper <- function(x) {eval_g_ineq(x, ...)} } else { eval_g_ineq_wrapper <- function(x) { list("constraints" = eval_g_ineq(x, ...), "jacobian" = eval_jac_g_ineq(x, ...)) } } # determine number of constraints tmp_constraints <- eval_g_ineq_wrapper(x0) if (is.list(tmp_constraints)) { num_constraints_ineq <- length(tmp_constraints$constraints) } else { num_constraints_ineq <- length(tmp_constraints) } } else { # define dummy function eval_g_ineq_wrapper <- NULL } # change the environment of the equality constraint functions that we're # calling num_constraints_eq <- 0 if (!is.null(eval_g_eq)) { # if eval_g_eq does not return a list, write a wrapper function # combining eval_g_eq and eval_jac_g_eq if (is.list(eval_g_eq(x0, ...)) || is.null(eval_jac_g_eq)) { eval_g_eq_wrapper <- function(x) {eval_g_eq(x, ...)} } else { eval_g_eq_wrapper <- function(x) { list("constraints" = eval_g_eq(x, ...), "jacobian" = eval_jac_g_eq(x, ...)) } } # determine number of constraints tmp_constraints <- eval_g_eq_wrapper(x0) if (is.list(tmp_constraints)) { num_constraints_eq <- length(tmp_constraints$constraints) } else { num_constraints_eq <- length(tmp_constraints) } } else { # define dummy function eval_g_eq_wrapper <- NULL } # extract local options from list of options if they exist if ("local_opts" %in% names(opts)) { res.opts.add <- nloptr.add.default.options( opts.user = opts$local_opts, x0 = x0, num_constraints_ineq = num_constraints_ineq, num_constraints_eq = num_constraints_eq ) local_opts <- res.opts.add$opts.user opts$local_opts <- NULL } else { local_opts <- NULL } # add defaults to list of options res.opts.add <- nloptr.add.default.options( opts.user = opts, x0 = x0, num_constraints_ineq = num_constraints_ineq, num_constraints_eq = num_constraints_eq ) opts <- res.opts.add$opts.user # add the termination criteria to the list termination_conditions <- res.opts.add$termination_conditions # print description of options if requested if (opts$print_options_doc) { nloptr.print.options(opts.user = opts) } # define list with all algorithms # nloptr.options.description is a data.frame with options that is loaded # when nloptr is loaded. nloptr.default.options <- nloptr.get.default.options() list_algorithms <- unlist( strsplit( nloptr.default.options[nloptr.default.options$name == "algorithm", "possible_values"], split = ", ", fixed = TRUE ) ) # run derivative checker if (opts$check_derivatives) { if (opts$algorithm %in% grep("NLOPT_[G,L]N", list_algorithms, value = TRUE)) { warning("Skipping derivative checker because algorithm '", opts$algorithm, "' does not use gradients.") } else { # check derivatives of objective function message("Checking gradients of objective function.") check.derivatives( .x = x0, func = function(x) {eval_f_wrapper(x)$objective}, func_grad = function(x) {eval_f_wrapper(x)$gradient}, check_derivatives_tol = opts$check_derivatives_tol, check_derivatives_print = opts$check_derivatives_print, func_grad_name = "eval_grad_f" ) if (num_constraints_ineq > 0) { # check derivatives of inequality constraints message("Checking gradients of inequality constraints.\n") check.derivatives( .x = x0, func = function(x) {eval_g_ineq_wrapper(x)$constraints}, func_grad = function(x) {eval_g_ineq_wrapper(x)$jacobian}, check_derivatives_tol = opts$check_derivatives_tol, check_derivatives_print = opts$check_derivatives_print, func_grad_name = "eval_jac_g_ineq" ) } if (num_constraints_eq > 0) { # check derivatives of equality constraints message("Checking gradients of equality constraints.\n") check.derivatives( .x = x0, func = function(x) {eval_g_eq_wrapper(x)$constraints}, func_grad = function(x) {eval_g_eq_wrapper(x)$jacobian}, check_derivatives_tol = opts$check_derivatives_tol, check_derivatives_print = opts$check_derivatives_print, func_grad_name = "eval_jac_g_eq" ) } } } ret <- list("x0" = x0, "eval_f" = eval_f_wrapper, "lower_bounds" = lb, "upper_bounds" = ub, "num_constraints_ineq" = num_constraints_ineq, "eval_g_ineq" = eval_g_ineq_wrapper, "num_constraints_eq" = num_constraints_eq, "eval_g_eq" = eval_g_eq_wrapper, "options" = opts, "local_options" = local_opts, "nloptr_environment" = new.env()) attr(ret, "class") <- "nloptr" # add the current call to the list ret$call <- match.call() # add the termination criteria to the list ret$termination_conditions <- termination_conditions # check whether we have a correctly formed nloptr object is.nloptr(ret) # Count the number of times that we try to solve the problem. num.evals <- 0 solve.continue <- TRUE while (num.evals <= 10 && solve.continue) { # Update the number of evaluations. num.evals <- num.evals + 1 # choose correct minimization function based on whether constrained were # supplied solution <- .Call(NLoptR_Optimize, ret) # remove the environment from the return object ret$environment <- NULL # add solution variables to object ret$status <- solution$status ret$message <- solution$message ret$iterations <- solution$iterations ret$objective <- solution$objective ret$solution <- solution$solution ret$version <- paste(c(solution$version_major, solution$version_minor, solution$version_bugfix), collapse = ".") ret$num.evals <- num.evals # If maxtime is set to a positive number in the options or if the return # status of the solver is not equal to 6, we can stop trying to solve # the problem. # # Solution status 6: NLOPT_MAXTIME_REACHED: Optimization stopped because # maxtime (above) was reached. # # This loop is needed because sometimes the solver exits with this code # even if maxtime is set to 0 or a negative number. if (opts$maxtime > 0 || solution$status != 6) { solve.continue <- FALSE } } ret # return call unnecessary; .Primitive return will be called. } nloptr/R/nloptr.add.default.options.R0000644000176200001440000000557114472612401017307 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: nloptr.add.default.options.R # Author: Jelmer Ypma # Date: 17 August 2016 # # Add default options to a user supplied list of options. # # Input: # opts.user: list with user defined options # x0: initial value for control variables # num_constraints_ineq: number of inequality constraints # num_constraints_eq: number of equality constraints # # Output: # opts.user with default options added for those options # that were not part of the original opts.user. # # CHANGELOG: # 2016-08-17: Fixed bug that sometimes caused segmentation faults due to # uninitialized tolerances for the (in)equality constraints # (thanks to Florian Schwendiger). # 2023-02-08: Tweaks for efficiency and readability (Avraham Adler) # nloptr.add.default.options <- function(opts.user, x0 = 0, num_constraints_ineq = 0, num_constraints_eq = 0) { nloptr.default.options <- nloptr.get.default.options() rownames(nloptr.default.options) <- nloptr.default.options$name # get names of options that define a termination condition termination.opts <- nloptr.default.options$name[ which(as.logical(nloptr.default.options$is_termination_condition)) ] if (sum(termination.opts %in% names(opts.user)) == 0) { # get default xtol_rel xtol_rel_default <- as.numeric( nloptr.default.options$default[ nloptr.default.options$name == "xtol_rel" ] ) warning("No termination criterion specified, using default", "(relative x-tolerance = ", xtol_rel_default, ")") termination_conditions <- paste0("relative x-tolerance = ", xtol_rel_default, " (DEFAULT)") } else { conv_options <- unlist(opts.user[names(opts.user) %in% termination.opts]) termination_conditions <- paste0(paste(names(conv_options)), ": ", paste(conv_options), collapse = "\t") } # determine list with names of options that contain character values. # we need to add quotes around these options below. nloptr.list.character.options <- nloptr.default.options$name[nloptr.default.options$type == "character"] opts <- vector(mode = "list", nrow(nloptr.default.options)) names(opts) <- nloptr.default.options$name for (name in names(opts)) { if (!is.null(opts.user[[name]])) { opts[[name]] <- opts.user[[name]] } else if (name %in% nloptr.list.character.options) { opts[[name]] <- nloptr.default.options[name, "default"] } else { opts[[name]] <- eval(parse(text = nloptr.default.options[name, "default"])) } } list("opts.user" = opts, "termination_conditions" = termination_conditions) } nloptr/R/nm.R0000644000176200001440000001333014472612401012527 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: nm.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Nelder-Mead and Subplex. # # CHANGELOG # 2023-02-09: Cleanup and tweaks for safety and efficiency (Avraham Adler) # #' Nelder-Mead Simplex #' #' An implementation of almost the original Nelder-Mead simplex algorithm. #' #' Provides explicit support for bound constraints, using essentially the method #' proposed in Box. Whenever a new point would lie outside the bound #' constraints the point is moved back exactly onto the constraint. #' #' @param x0 starting point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param lower,upper lower and upper bound constraints. #' @param nl.info logical; shall the original NLopt info been shown. #' @param control list of options, see \code{nl.opts} for help. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export neldermead #' #' @author Hans W. Borchers #' #' @note The author of NLopt would tend to recommend the Subplex method #' instead. #' #' @seealso \code{dfoptim::nmk} #' #' @references J. A. Nelder and R. Mead, ``A simplex method for function #' minimization,'' The Computer Journal 7, p. 308-313 (1965). #' #' M. J. Box, ``A new method of constrained optimization and a comparison with #' other methods,'' Computer J. 8 (1), 42-52 (1965). #' #' @examples #' #' # Fletcher and Powell's helic valley #' fphv <- function(x) #' 100*(x[3] - 10*atan2(x[2], x[1])/(2*pi))^2 + #' (sqrt(x[1]^2 + x[2]^2) - 1)^2 +x[3]^2 #' x0 <- c(-1, 0, 0) #' neldermead(x0, fphv) # 1 0 0 #' #' # Powell's Singular Function (PSF) #' psf <- function(x) (x[1] + 10*x[2])^2 + 5*(x[3] - x[4])^2 + #' (x[2] - 2*x[3])^4 + 10*(x[1] - x[4])^4 #' x0 <- c(3, -1, 0, 1) #' neldermead(x0, psf) # 0 0 0 0, needs maximum number of function calls #' #' \dontrun{ #' # Bounded version of Nelder-Mead #' rosenbrock <- function(x) { ## Rosenbrock Banana function #' 100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2 + #' 100 * (x[3] - x[2]^2)^2 + (1 - x[2])^2 #' } #' lower <- c(-Inf, 0, 0) #' upper <- c( Inf, 0.5, 1) #' x0 <- c(0, 0.1, 0.1) #' S <- neldermead(c(0, 0.1, 0.1), rosenbrock, lower, upper, nl.info = TRUE) #' # $xmin = c(0.7085595, 0.5000000, 0.2500000) #' # $fmin = 0.3353605} #' neldermead <- function(x0, fn, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LN_NELDERMEAD" fun <- match.fun(fn) fn <- function(x) fun(x, ...) S0 <- nloptr(x0, fn, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } #' Subplex Algorithm #' #' Subplex is a variant of Nelder-Mead that uses Nelder-Mead on a sequence of #' subspaces. #' #' SUBPLEX is claimed to be much more efficient and robust than the original #' Nelder-Mead while retaining the latter's facility with discontinuous #' objectives. #' #' This implementation has explicit support for bound constraints via the #' method in the Box paper as described on the \code{neldermead} help page. #' #' @param x0 starting point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param lower,upper lower and upper bound constraints. #' @param nl.info logical; shall the original NLopt info been shown. #' @param control list of options, see \code{nl.opts} for help. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export sbplx #' #' @note It is the request of Tom Rowan that reimplementations of his algorithm #' shall not use the name `subplex'. #' #' @seealso \code{subplex::subplex} #' #' @references T. Rowan, ``Functional Stability Analysis of Numerical #' Algorithms'', Ph.D. thesis, Department of Computer Sciences, University of #' Texas at Austin, 1990. #' #' @examples #' #' # Fletcher and Powell's helic valley #' fphv <- function(x) #' 100*(x[3] - 10*atan2(x[2], x[1])/(2*pi))^2 + #' (sqrt(x[1]^2 + x[2]^2) - 1)^2 +x[3]^2 #' x0 <- c(-1, 0, 0) #' sbplx(x0, fphv) # 1 0 0 #' #' # Powell's Singular Function (PSF) #' psf <- function(x) (x[1] + 10*x[2])^2 + 5*(x[3] - x[4])^2 + #' (x[2] - 2*x[3])^4 + 10*(x[1] - x[4])^4 #' x0 <- c(3, -1, 0, 1) #' sbplx(x0, psf, control = list(maxeval = Inf, ftol_rel = 1e-6)) # 0 0 0 0 (?) #' sbplx <- function(x0, fn, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LN_SBPLX" fun <- match.fun(fn) fn <- function(x) fun(x, ...) S0 <- nloptr(x0, fn, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/nloptions.R0000644000176200001440000000403714472612401014146 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: nloptions.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Function to define nloptr options list. #' Setting NL Options #' #' Sets and changes the NLOPT options. #' #' The following options can be set (here with default values): #' #' \code{stopval = -Inf, # stop minimization at this value}\cr \code{xtol_rel = #' 1e-6, # stop on small optimization step}\cr \code{maxeval = 1000, # stop on #' this many function evaluations}\cr \code{ftol_rel = 0.0, # stop on change #' times function value}\cr \code{ftol_abs = 0.0, # stop on small change of #' function value}\cr \code{check_derivatives = FALSE} #' #' @param optlist list of options, see below. #' #' @return returns a list with default and changed options. #' #' @export #' #' @author Hans W. Borchers #' #' @note There are more options that can be set for solvers in NLOPT. These #' cannot be set through their wrapper functions. To see the full list of #' options and algorithms, type \code{nloptr.print.options()}. #' #' @examples #' #' nl.opts(list(xtol_rel = 1e-8, maxeval = 2000)) #' nl.opts <- function(optlist = NULL) { opts <- list( stopval = -Inf, # stop minimization at this value xtol_rel = 1e-6, # stop on small optimization step maxeval = 1000, # stop on this many function evaluations ftol_rel = 0.0, # stop on change times function value ftol_abs = 0.0, # stop on small change of function value check_derivatives = FALSE, algorithm = NULL # will be filled by each single function ) if (is.null(optlist)) return(opts) if (!is.list(optlist) || "" %in% names(optlist)) stop("Argument `optlist` must be a named list.") for (option_name in names(optlist)) { opts[[option_name]] <- optlist[[option_name]] } if (!is.null(opts[["algorithm"]])) { warning("Option `algorithm` cannot be set here. It will be overwritten.") opts[["algorithm"]] <- NULL } opts } nloptr/R/cobyla.R0000644000176200001440000002322714634272373013406 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: cobyla.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using COBYLA, BOBYQA, and NEWUOA. # # CHANGELOG # 2023-02-10: Tweaks for efficiency and readability (Avraham Adler) # 2024-06-04: Switched desired direction of the hin/hinjac inequalities, leaving # the old behavior as the default for now. Also cleaned up the HS100 # example (Avraham Adler). # #' Constrained Optimization by Linear Approximations #' #' \acronym{COBYLA} is an algorithm for derivative-free optimization with #' nonlinear inequality and equality constraints (but see below). #' #' It constructs successive linear approximations of the objective function and #' constraints via a simplex of \eqn{n+1} points (in \eqn{n} dimensions), and #' optimizes these approximations in a trust region at each step. #' #' \acronym{COBYLA} supports equality constraints by transforming them into two #' inequality constraints. This functionality has not been added to the wrapper. #' To use \acronym{COBYLA} with equality constraints, please use the full #' \code{nloptr} invocation. #' #' @param x0 starting point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param lower,upper lower and upper bound constraints. #' @param hin function defining the inequality constraints, that is #' \code{hin>=0} for all components. #' @param nl.info logical; shall the original \acronym{NLopt} info be shown. #' @param control list of options, see \code{nl.opts} for help. #' @param deprecatedBehavior logical; if \code{TRUE} (default for now), the old #' behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} #' instead of \eqn{\le 0}. This will be reversed in a future release and #' eventually removed. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @author Hans W. Borchers #' #' @note The original code, written in Fortran by Powell, was converted in C #' for the \acronym{SciPy} project. #' #' @seealso \code{\link{bobyqa}}, \code{\link{newuoa}} #' #' @references M. J. D. Powell, ``A direct search optimization method that #' models the objective and constraint functions by linear interpolation,'' in #' Advances in Optimization and Numerical Analysis, eds. S. Gomez and J.-P. #' Hennart (Kluwer Academic: Dordrecht, 1994), p. 51-67. #' #' @examples #' #' ## Solve the Hock-Schittkowski problem no. 100 with analytic gradients #' ## See https://apmonitor.com/wiki/uploads/Apps/hs100.apm #' #' x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) #' fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + #' 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + #' x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} #' #' hin.hs100 <- function(x) {c( #' 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, #' 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, #' 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, #' 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - #' 11 * x[7]) #' } #' #' S <- cobyla(x0.hs100, fn.hs100, hin = hin.hs100, #' nl.info = TRUE, control = list(xtol_rel = 1e-8, maxeval = 2000), #' deprecatedBehavior = FALSE) #' #' ## The optimum value of the objective function should be 680.6300573 #' ## A suitable parameter vector is roughly #' ## (2.330, 1.9514, -0.4775, 4.3657, -0.6245, 1.0381, 1.5942) #' #' S #' #' @export cobyla #' cobyla <- function(x0, fn, lower = NULL, upper = NULL, hin = NULL, nl.info = FALSE, control = list(), deprecatedBehavior = TRUE, ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LN_COBYLA" f1 <- match.fun(fn) fn <- function(x) f1(x, ...) if (!is.null(hin)) { if (deprecatedBehavior) { warning("The old behavior for hin >= 0 has been deprecated. Please ", "restate the inequality to be <=0. The ability to use the old ", "behavior will be removed in a future release.") .hin <- match.fun(hin) hin <- function(x) -.hin(x, ...) # change hin >= 0 to hin <= 0 ! } } S0 <- nloptr(x0, eval_f = fn, lb = lower, ub = upper, eval_g_ineq = hin, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } #' Bound Optimization by Quadratic Approximation #' #' \acronym{BOBYQA} performs derivative-free bound-constrained optimization #' using an iteratively constructed quadratic approximation for the objective #' function. #' #' This is an algorithm derived from the \acronym{BOBYQA} Fortran subroutine of #' Powell, converted to C and modified for the \acronym{NLopt} stopping #' criteria. #' #' @param x0 starting point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param lower,upper lower and upper bound constraints. #' @param nl.info logical; shall the original \acronym{NLopt} info be shown. #' @param control list of options, see \code{nl.opts} for help. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by \acronym{NLopt} and giving #' additional information.} #' #' @export bobyqa #' #' @note Because \acronym{BOBYQA} constructs a quadratic approximation of the #' objective, it may perform poorly for objective functions that are not #' twice-differentiable. #' #' @seealso \code{\link{cobyla}}, \code{\link{newuoa}} #' #' @references M. J. D. Powell. ``The BOBYQA algorithm for bound constrained #' optimization without derivatives,'' Department of Applied Mathematics and #' Theoretical Physics, Cambridge England, technical reportNA2009/06 (2009). #' #' @examples #' #' ## Rosenbrock Banana function #' #' rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2} #' #' ## The function as written above has a minimum of 0 at (1, 1) #' #' S <- bobyqa(c(0, 0), rbf) #' #' #' S #' #' ## Rosenbrock Banana function with both parameters constrained to [0, 0.5] #' #' S <- bobyqa(c(0, 0), rbf, lower = c(0, 0), upper = c(0.5, 0.5)) #' #' S #' bobyqa <- function(x0, fn, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LN_BOBYQA" fun <- match.fun(fn) fn <- function(x) fun(x, ...) S0 <- nloptr(x0, fn, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } #' New Unconstrained Optimization with quadratic Approximation #' #' \acronym{NEWUOA} solves quadratic subproblems in a spherical trust region via #' a truncated conjugate-gradient algorithm. For bound-constrained problems, #' \acronym{BOBYQA} should be used instead, as Powell developed it as an #' enhancement thereof for bound constraints. #' #' This is an algorithm derived from the \acronym{NEWUOA} Fortran subroutine of #' Powell, converted to C and modified for the \acronym{NLopt} stopping #' criteria. #' #' @param x0 starting point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param nl.info logical; shall the original \acronym{NLopt} info be shown. #' @param control list of options, see \code{nl.opts} for help. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export newuoa #' #' @author Hans W. Borchers #' #' @note \acronym{NEWUOA} may be largely superseded by \acronym{BOBYQA}. #' #' @seealso \code{\link{bobyqa}}, \code{\link{cobyla}} #' #' @references M. J. D. Powell. ``The BOBYQA algorithm for bound constrained #' optimization without derivatives,'' Department of Applied Mathematics and #' Theoretical Physics, Cambridge England, technical reportNA2009/06 (2009). #' #' @examples #' #' ## Rosenbrock Banana function #' #' rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2} #' #' S <- newuoa(c(1, 2), rbf) #' #' ## The function as written above has a minimum of 0 at (1, 1) #' #' S #' newuoa <- function(x0, fn, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LN_NEWUOA" fun <- match.fun(fn) fn <- function(x) fun(x, ...) S0 <- nloptr(x0, fn, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/global.R0000644000176200001440000002743614634272373013403 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: global.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using StoGo. # # CHANGELOG # # 2023-02-08: Tweaks for efficiency and readability. (Avraham Adler) # 2024-06-04: Switched desired direction of the hin/hinjac inequalities, leaving # the old behavior as the default for now. Also cleaned up the Hartmann 6 # example. (Avraham Adler) # #----------------------------------StoGo---------------------------------------- #' Stochastic Global Optimization #' #' \acronym{StoGO} is a global optimization algorithm that works by #' systematically dividing the search space---which must be #' bound-constrained---into smaller hyper-rectangles via a branch-and-bound #' technique, and searching them using a gradient-based local-search algorithm #' (a \acronym{BFGS} variant), optionally including some randomness. #' #' @param x0 initial point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param gr optional gradient of the objective function. #' @param lower,upper lower and upper bound constraints. #' @param maxeval maximum number of function evaluations. #' @param xtol_rel stopping criterion for relative change reached. #' @param randomized logical; shall a randomizing variant be used? #' @param nl.info logical; shall the original \acronym{NLopt} info be shown. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by \acronym{NLopt} and giving #' additional information.} #' #' @export stogo #' #' @author Hans W. Borchers #' #' @note Only bounds-constrained problems are supported by this algorithm. #' #' @references S. Zertchaninov and K. Madsen, ``A C++ Programme for Global #' Optimization,'' IMM-REP-1998-04, Department of Mathematical Modelling, #' Technical University of Denmark. #' #' @examples #' #' ## Rosenbrock Banana objective function #' #' rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2} #' #' x0 <- c(-1.2, 1) #' lb <- c(-3, -3) #' ub <- c(3, 3) #' #' ## The function as written above has a minimum of 0 at (1, 1) #' #' stogo(x0 = x0, fn = rbf, lower = lb, upper = ub) #' stogo <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, maxeval = 10000, xtol_rel = 1e-6, randomized = FALSE, nl.info = FALSE, ...) { opts <- list() opts$maxeval <- maxeval opts$xtol_rel <- xtol_rel if (randomized) { opts["algorithm"] <- "NLOPT_GD_STOGO_RAND" } else { opts["algorithm"] <- "NLOPT_GD_STOGO" } fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (is.null(gr)) {gr <- function(x) nl.grad(x, fn)} S0 <- nloptr(x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } #---------------------------------ISRES----------------------------------------- # ISRES supports nonlinear constraints but mat be quite inaccurate! #' Improved Stochastic Ranking Evolution Strategy #' #' The Improved Stochastic Ranking Evolution Strategy (\acronym{ISRES}) is an #' algorithm for nonlinearly constrained global optimization, or at least #' semi-global, although it has heuristics to escape local optima. #' #' The evolution strategy is based on a combination of a mutation rule---with a #' log-normal step-size update and exponential smoothing---and differential #' variation---a Nelder-Mead-like update rule). The fitness ranking is simply #' via the objective function for problems without nonlinear constraints, but #' when nonlinear constraints are included the stochastic ranking proposed by #' Runarsson and Yao is employed. #' #' This method supports arbitrary nonlinear inequality and equality constraints #' in addition to the bounds constraints. #' #' @param x0 initial point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param lower,upper lower and upper bound constraints. #' @param hin function defining the inequality constraints, that is #' \code{hin <= 0} for all components. #' @param heq function defining the equality constraints, that is \code{heq = 0} #' for all components. #' @param maxeval maximum number of function evaluations. #' @param pop.size population size. #' @param xtol_rel stopping criterion for relative change reached. #' @param nl.info logical; shall the original \acronym{NLopt} info be shown. #' @param deprecatedBehavior logical; if \code{TRUE} (default for now), the old #' behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} #' instead of \eqn{\le 0}. This will be reversed in a future release and #' eventually removed. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export isres #' #' @author Hans W. Borchers #' #' @note The initial population size for CRS defaults to \eqn{20x(n+1)} in #' \eqn{n} dimensions, but this can be changed. The initial population must be #' at least \eqn{n+1}. #' #' @references Thomas Philip Runarsson and Xin Yao, ``Search biases in #' constrained evolutionary optimization,'' IEEE Trans. on Systems, Man, and #' Cybernetics Part C: Applications and Reviews, vol. 35 (no. 2), pp. 233-243 #' (2005). #' #' @examples #' #' ## Rosenbrock Banana objective function #' #' rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2} #' #' x0 <- c(-1.2, 1) #' lb <- c(-3, -3) #' ub <- c(3, 3) #' #' ## The function as written above has a minimum of 0 at (1, 1) #' #' isres(x0 = x0, fn = rbf, lower = lb, upper = ub) #' #' ## Now subject to the inequality that x[1] + x[2] <= 1.5 #' #' hin <- function(x) {x[1] + x[2] - 1.5} #' #' S <- isres(x0 = x0, fn = rbf, hin = hin, lower = lb, upper = ub, #' maxeval = 2e5L, deprecatedBehavior = FALSE) #' #' S #' #' sum(S$par) #' isres <- function(x0, fn, lower, upper, hin = NULL, heq = NULL, maxeval = 10000, pop.size = 20 * (length(x0) + 1), xtol_rel = 1e-6, nl.info = FALSE, deprecatedBehavior = TRUE, ...) { opts <- list() opts$maxeval <- maxeval opts$xtol_rel <- xtol_rel opts$population <- pop.size opts$algorithm <- "NLOPT_GN_ISRES" fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (!is.null(hin)) { if (deprecatedBehavior) { warning("The old behavior for hin >= 0 has been deprecated. Please ", "restate the inequality to be <=0. The ability to use the old ", "behavior will be removed in a future release.") .hin <- match.fun(hin) hin <- function(x) -.hin(x, ...) # change hin >= 0 to hin <= 0 ! } } if (!is.null(heq)) { .heq <- match.fun(heq) heq <- function(x) .heq(x) } S0 <- nloptr(x0 = x0, eval_f = fn, lb = lower, ub = upper, eval_g_ineq = hin, eval_g_eq = heq, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } #- --------------------------------- CRS -------------------------------------- #' Controlled Random Search #' #' The Controlled Random Search (\acronym{CRS}) algorithm (and in particular, #' the \acronym{CRS2} variant) with the `local mutation' modification. #' #' The \acronym{CRS} algorithms are sometimes compared to genetic algorithms, in #' that they start with a random population of points, and randomly evolve these #' points by heuristic rules. In this case, the evolution somewhat resembles a #' randomized Nelder-Mead algorithm. #' #' The published results for \acronym{CRS} seem to be largely empirical. #' #' @param x0 initial point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param lower,upper lower and upper bound constraints. #' @param maxeval maximum number of function evaluations. #' @param pop.size population size. #' @param ranseed prescribe seed for random number generator. #' @param xtol_rel stopping criterion for relative change reached. #' @param nl.info logical; shall the original \acronym{NLopt} info be shown. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by \acronym{NLopt} and giving #' additional information.} #' #' @export crs2lm #' #' @note The initial population size for CRS defaults to \eqn{10x(n+1)} in #' \eqn{n} dimensions, but this can be changed. The initial population must be #' at least \eqn{n+1}. #' #' @references W. L. Price, ``Global optimization by controlled random #' search,'' J. Optim. Theory Appl. 40 (3), p. 333-348 (1983). #' #' P. Kaelo and M. M. Ali, ``Some variants of the controlled random search #' algorithm for global optimization,'' J. Optim. Theory Appl. 130 (2), 253-264 #' (2006). #' #' @examples #' #' ## Minimize the Hartmann 6-Dimensional function #' ## See https://www.sfu.ca/~ssurjano/hart6.html #' #' a <- c(1.0, 1.2, 3.0, 3.2) #' A <- matrix(c(10, 0.05, 3, 17, #' 3, 10, 3.5, 8, #' 17, 17, 1.7, 0.05, #' 3.5, 0.1, 10, 10, #' 1.7, 8, 17, 0.1, #' 8, 14, 8, 14), nrow = 4) #' #' B <- matrix(c(.1312, .2329, .2348, .4047, #' .1696, .4135, .1451, .8828, #' .5569, .8307, .3522, .8732, #' .0124, .3736, .2883, .5743, #' .8283, .1004, .3047, .1091, #' .5886, .9991, .6650, .0381), nrow = 4) #' #' hartmann6 <- function(x, a, A, B) { #' fun <- 0 #' for (i in 1:4) { #' fun <- fun - a[i] * exp(-sum(A[i, ] * (x - B[i, ]) ^ 2)) #' } #' #' fun #' } #' #' ## The function has a global minimum of -3.32237 at #' ## (0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573) #' #' S <- crs2lm(x0 = rep(0, 6), hartmann6, lower = rep(0, 6), upper = rep(1, 6), #' ranseed = 10L, nl.info = TRUE, xtol_rel=1e-8, maxeval = 10000, #' a = a, A = A, B = B) #' #' S #' crs2lm <- function(x0, fn, lower, upper, maxeval = 10000, pop.size = 10 * (length(x0) + 1), ranseed = NULL, xtol_rel = 1e-6, nl.info = FALSE, ...) { opts <- list() opts$maxeval <- maxeval opts$xtol_rel <- xtol_rel opts$population <- pop.size if (!is.null(ranseed)) {opts$ranseed <- as.integer(ranseed)} opts$algorithm <- "NLOPT_GN_CRS2_LM" fun <- match.fun(fn) fn <- function(x) fun(x, ...) S0 <- nloptr(x0, eval_f = fn, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/auglag.R0000644000176200001440000002262414634272373013375 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: auglag.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Augmented Lagrangian. # # CHANGELOG # # 2017-09-26: Fixed bug, BOBYQA is allowed as local solver # (thanks to Leo Belzile). # 2023-02-08: Tweaks for efficiency and readability (Avraham Adler) # 2024-06-04: Switched desired direction of the hin/hinjac inequalities, leaving # the old behavior as the default for now. Also corrected Powell example. # (Avraham Adler) # #' Augmented Lagrangian Algorithm #' #' The Augmented Lagrangian method adds additional terms to the unconstrained #' objective function, designed to emulate a Lagrangian multiplier. #' #' This method combines the objective function and the nonlinear #' inequality/equality constraints (if any) in to a single function: #' essentially, the objective plus a `penalty' for any violated constraints. #' #' This modified objective function is then passed to another optimization #' algorithm with no nonlinear constraints. If the constraints are violated by #' the solution of this sub-problem, then the size of the penalties is #' increased and the process is repeated; eventually, the process must converge #' to the desired solution (if it exists). #' #' Since all of the actual optimization is performed in this subsidiary #' optimizer, the subsidiary algorithm that you specify determines whether the #' optimization is gradient-based or derivative-free. #' #' The local solvers available at the moment are ``COBYLA'' (for the #' derivative-free approach) and ``LBFGS'', ``MMA'', or ``SLSQP'' (for smooth #' functions). The tolerance for the local solver has to be provided. #' #' There is a variant that only uses penalty functions for equality constraints #' while inequality constraints are passed through to the subsidiary algorithm #' to be handled directly; in this case, the subsidiary algorithm must handle #' inequality constraints. (At the moment, this variant has been turned off #' because of problems with the NLOPT library.) #' #' @param x0 starting point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param gr gradient of the objective function; will be provided provided is #' \code{NULL} and the solver requires derivatives. #' @param lower,upper lower and upper bound constraints. #' @param hin,hinjac defines the inequality constraints, \code{hin(x) >= 0} #' @param heq,heqjac defines the equality constraints, \code{heq(x) = 0}. #' @param localsolver available local solvers: COBYLA, LBFGS, MMA, or SLSQP. #' @param localtol tolerance applied in the selected local solver. #' @param ineq2local logical; shall the inequality constraints be treated by #' the local solver?; not possible at the moment. #' @param nl.info logical; shall the original NLopt info been shown. #' @param control list of options, see \code{nl.opts} for help. #' @param deprecatedBehavior logical; if \code{TRUE} (default for now), the old #' behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} #' instead of \eqn{\le 0}. This will be reversed in a future release and #' eventually removed. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{global_solver}{the global NLOPT solver used.} #' \item{local_solver}{the local NLOPT solver used, LBFGS or COBYLA.} #' \item{convergence}{integer code indicating successful completion #' (> 0) or a possible error number (< 0).} #' \item{message}{character string produced by NLopt and giving additional #' information.} #' #' @export #' #' @author Hans W. Borchers #' #' @note Birgin and Martinez provide their own free implementation of the #' method as part of the TANGO project; other implementations can be found in #' semi-free packages like LANCELOT. #' #' @seealso \code{alabama::auglag}, \code{Rsolnp::solnp} #' #' @references Andrew R. Conn, Nicholas I. M. Gould, and Philippe L. Toint, ``A #' globally convergent augmented Lagrangian algorithm for optimization with #' general constraints and simple bounds,'' SIAM J. Numer. Anal. vol. 28, no. #' 2, p. 545-572 (1991). #' #' E. G. Birgin and J. M. Martinez, ``Improving ultimate convergence of an #' augmented Lagrangian method," Optimization Methods and Software vol. 23, no. #' 2, p. 177-195 (2008). #' #' @examples #' #' x0 <- c(1, 1) #' fn <- function(x) (x[1] - 2) ^ 2 + (x[2] - 1) ^ 2 #' hin <- function(x) 0.25 * x[1]^2 + x[2] ^ 2 - 1 # hin <= 0 #' heq <- function(x) x[1] - 2 * x[2] + 1 # heq = 0 #' gr <- function(x) nl.grad(x, fn) #' hinjac <- function(x) nl.jacobian(x, hin) #' heqjac <- function(x) nl.jacobian(x, heq) #' #' # with COBYLA #' auglag(x0, fn, gr = NULL, hin = hin, heq = heq, deprecatedBehavior = FALSE) #' #' # $par: 0.8228761 0.9114382 #' # $value: 1.393464 #' # $iter: 1001 #' #' auglag(x0, fn, gr = NULL, hin = hin, heq = heq, localsolver = "SLSQP", #' deprecatedBehavior = FALSE) #' #' # $par: 0.8228757 0.9114378 #' # $value: 1.393465 #' # $iter 184 #' #' ## Example from the alabama::auglag help page #' ## Parameters should be roughly (0, 0, 1) with an objective value of 1. #' #' fn <- function(x) (x[1] + 3 * x[2] + x[3]) ^ 2 + 4 * (x[1] - x[2]) ^ 2 #' heq <- function(x) x[1] + x[2] + x[3] - 1 #' # hin restated from alabama example to be <= 0. #' hin <- function(x) c(-6 * x[2] - 4 * x[3] + x[1] ^ 3 + 3, -x[1], -x[2], -x[3]) #' #' set.seed(12) #' auglag(runif(3), fn, hin = hin, heq = heq, localsolver= "lbfgs", #' deprecatedBehavior = FALSE) #' #' # $par: 4.861756e-08 4.732373e-08 9.999999e-01 #' # $value: 1 #' # $iter: 145 #' #' ## Powell problem from the Rsolnp::solnp help page #' ## Parameters should be roughly (-1.7171, 1.5957, 1.8272, -0.7636, -0.7636) #' ## with an objective value of 0.0539498478. #' #' x0 <- c(-2, 2, 2, -1, -1) #' fn1 <- function(x) exp(x[1] * x[2] * x[3] * x[4] * x[5]) #' eqn1 <-function(x) #' c(x[1] * x[1] + x[2] * x[2] + x[3] * x[3] + x[4] * x[4] + x[5] * x[5] - 10, #' x[2] * x[3] - 5 * x[4] * x[5], #' x[1] * x[1] * x[1] + x[2] * x[2] * x[2] + 1) #' #' auglag(x0, fn1, heq = eqn1, localsolver = "mma", deprecatedBehavior = FALSE) #' #' # $par: -1.7173645 1.5959655 1.8268352 -0.7636185 -0.7636185 #' # $value: 0.05394987 #' # $iter: 916 #' auglag <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, heq = NULL, heqjac = NULL, localsolver = "COBYLA", localtol = 1e-6, ineq2local = FALSE, nl.info = FALSE, control = list(), deprecatedBehavior = TRUE, ...) { if (ineq2local) { # gsolver <- "NLOPT_LN_AUGLAG_EQ" stop("Inequalities to local solver: feature not yet implemented.") } localsolver <- toupper(localsolver) if (localsolver %in% c("COBYLA", "BOBYQA")) { # derivative-free dfree <- TRUE gsolver <- "NLOPT_LN_AUGLAG" lsolver <- paste0("NLOPT_LN_", localsolver) } else if (localsolver %in% c("LBFGS", "MMA", "SLSQP")) { # with derivatives dfree <- FALSE gsolver <- "NLOPT_LD_AUGLAG" lsolver <- paste0("NLOPT_LD_", localsolver) } else { stop("Only local solvers allowed: BOBYQA, COBYLA, LBFGS, MMA, SLSQP.") } # Function and gradient, if needed .fn <- match.fun(fn) fn <- function(x) .fn(x, ...) if (!dfree && is.null(gr)) {gr <- function(x) nl.grad(x, fn)} # Global and local options opts <- nl.opts(control) opts$algorithm <- gsolver local_opts <- list(algorithm = lsolver, xtol_rel = localtol, eval_grad_f = if (!dfree) gr else NULL) opts$local_opts <- local_opts # Inequality constraints if (!is.null(hin)) { if (deprecatedBehavior) { warning("The old behavior for hin >= 0 has been deprecated. Please ", "restate the inequality to be <=0. The ability to use the old ", "behavior will be removed in a future release.") .hin <- match.fun(hin) hin <- function(x) -.hin(x, ...) # change hin >= 0 to hin <= 0 ! } } if (!dfree) { if (is.null(hinjac)) { hinjac <- function(x) nl.jacobian(x, hin) } else if (deprecatedBehavior) { warning("The old behavior for hinjac >= 0 has been deprecated. Please ", "restate the inequality to be <=0. The ability to use the old ", "behavior will be removed in a future release.") .hinjac <- match.fun(hinjac) hinjac <- function(x) -.hinjac(x) } } # Equality constraints if (!is.null(heq)) { .heq <- match.fun(heq) heq <- function(x) .heq(x) } if (!dfree) { if (is.null(heqjac)) { heqjac <- function(x) nl.jacobian(x, heq) } else { .heqjac <- match.fun(heqjac) heqjac <- function(x) .heqjac(x) } } S0 <- nloptr(x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, eval_g_ineq = hin, eval_jac_g_ineq = hinjac, eval_g_eq = heq, eval_jac_g_eq = heqjac, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, global_solver = gsolver, local_solver = lsolver, convergence = S0$status, message = S0$message) } nloptr/R/is.nloptr.R0000644000176200001440000002211414763300100014036 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: is.nloptr.R # Author: Jelmer Ypma # Date: 10 June 2010 # # Input: object # Output: bool telling whether the object is an nloptr or not # # CHANGELOG # 2011-06-16: separated local optimizer check and equality constraints check # 2014-05-05: Replaced cat by warning. # 2023-02-08: Tweaks for efficiency and readability (Avraham Adler) # #' R interface to NLopt #' #' is.nloptr preforms checks to see if a fully specified problem is supplied to #' nloptr. Mostly for internal use. #' #' @param x object to be tested. #' #' @return Logical. Return TRUE if all tests were passed, otherwise return #' FALSE or exit with Error. #' #' @export is.nloptr #' #' @author Jelmer Ypma #' #' @seealso \code{\link[nloptr:nloptr]{nloptr}} #' #' @keywords optimize interface is.nloptr <- function(x) { # Check whether the object exists and is a list if (is.null(x)) return(FALSE) # Proper use of return to break out early :) if (!is.list(x)) return(FALSE) # Helper values now that we are certain x is a list lx0 <- length(x$x0) # Check whether the needed wrapper functions are supplied if (!is.function(x$eval_f)) stop("eval_f is not a function") if (!is.null(x$eval_g_ineq) && !is.function(x$eval_g_ineq)) stop("eval_g_ineq is not a function") if (!is.null(x$eval_g_eq) && !is.function(x$eval_g_eq)) stop("eval_g_eq is not a function") # Check whether bounds are defined for all controls if (anyNA(x$x0)) stop("x0 contains NA") if (lx0 != length(x$lower_bounds)) stop("length(lb) != length(x0)") if (lx0 != length(x$upper_bounds)) stop("length(ub) != length(x0)") # Check whether the initial value is within the bounds if (any(x$x0 < x$lower_bounds)) {stop("at least one element in x0 < lb")} if (any(x$x0 > x$upper_bounds)) {stop("at least one element in x0 > ub")} # define list with all algorithms list_algorithms <- c( "NLOPT_GN_DIRECT", "NLOPT_GN_DIRECT_L", "NLOPT_GN_DIRECT_L_RAND", "NLOPT_GN_DIRECT_NOSCAL", "NLOPT_GN_DIRECT_L_NOSCAL", "NLOPT_GN_DIRECT_L_RAND_NOSCAL", "NLOPT_GN_ORIG_DIRECT", "NLOPT_GN_ORIG_DIRECT_L", "NLOPT_GD_STOGO", "NLOPT_GD_STOGO_RAND", "NLOPT_LD_SLSQP", if (have.nlopt.ld.lbfgs.nocedal) "NLOPT_LD_LBFGS_NOCEDAL", "NLOPT_LD_LBFGS", "NLOPT_LN_PRAXIS", "NLOPT_LD_VAR1", "NLOPT_LD_VAR2", "NLOPT_LD_TNEWTON", "NLOPT_LD_TNEWTON_RESTART", "NLOPT_LD_TNEWTON_PRECOND", "NLOPT_LD_TNEWTON_PRECOND_RESTART", "NLOPT_GN_CRS2_LM", "NLOPT_GN_MLSL", "NLOPT_GD_MLSL", "NLOPT_GN_MLSL_LDS", "NLOPT_GD_MLSL_LDS", "NLOPT_LD_MMA", "NLOPT_LD_CCSAQ", "NLOPT_LN_COBYLA", "NLOPT_LN_NEWUOA", "NLOPT_LN_NEWUOA_BOUND", "NLOPT_LN_NELDERMEAD", "NLOPT_LN_SBPLX", "NLOPT_LN_AUGLAG", "NLOPT_LD_AUGLAG", "NLOPT_LN_AUGLAG_EQ", "NLOPT_LD_AUGLAG_EQ", "NLOPT_LN_BOBYQA", "NLOPT_GN_ISRES", "NLOPT_GN_ESCH" ) # check if an existing algorithm was supplied if (!(x$options$algorithm %in% list_algorithms)) { stop("Incorrect algorithm supplied. Use one of the following:\n", paste(list_algorithms, collapse = "\n")) } # determine subset of algorithms that need a derivative list_algorithms_d <- list_algorithms[grep("NLOPT_[G,L]D", list_algorithms)] list_algorithms_n <- list_algorithms[grep("NLOPT_[G,L]N", list_algorithms)] # Check the whether we don't have NA's if we evaluate the objective function # in x0 f0 <- x$eval_f(x$x0) if (is.list(f0)) { if (is.na(f0$objective)) stop("objective in x0 returns NA") if (anyNA(f0$gradient)) stop("gradient of objective in x0 returns NA") if (length(f0$gradient) != lx0) { stop("wrong number of elements in gradient of objective") } # check whether algorithm needs a derivative if (x$options$algorithm %in% list_algorithms_n) { warning("a gradient was supplied for the objective function, ", "but algorithm ", x$options$algorithm, " does not use gradients.") } } else { if (anyNA(f0)) stop("objective in x0 returns NA") # check whether algorithm needs a derivative if (x$options$algorithm %in% list_algorithms_d) { stop("A gradient for the objective function is needed by ", "algorithm ", x$options$algorithm, " but was not supplied.\n") } } # Check the whether we don't have NA's if we evaluate the inequality # constraints in x0 if (!is.null(x$eval_g_ineq)) { g0_ineq <- x$eval_g_ineq(x$x0) if (is.list(g0_ineq)) { if (anyNA(g0_ineq$constraints)) { stop("inequality constraints in x0 returns NA") } if (anyNA(g0_ineq$jacobian)) { stop("jacobian of inequality constraints in x0 returns NA") } if (length(g0_ineq$jacobian) != length(g0_ineq$constraints) * lx0) { stop("wrong number of elements in jacobian of inequality ", "constraints (is ", length(g0_ineq$jacobian), ", but should be ", length(g0_ineq$constraints), " x ", lx0, " = ", length(g0_ineq$constraints) * lx0, ")") } # check whether algorithm needs a derivative if (x$options$algorithm %in% list_algorithms_n) { warning("a gradient was supplied for the inequality ", "constraints, but algorithm ", x$options$algorithm, " does not use gradients.") } } else { if (anyNA(g0_ineq)) stop("inequality constraints in x0 returns NA") # check whether algorithm needs a derivative if (x$options$algorithm %in% list_algorithms_d) { stop("A gradient for the inequality constraints is needed by ", "algorithm ", x$options$algorithm, " but was not supplied.\n") } } } # Check the whether we don"t have NA"s if we evaluate the equality # constraints in x0 if (!is.null(x$eval_g_eq)) { g0_eq <- x$eval_g_eq(x$x0) if (is.list(g0_eq)) { if (anyNA(g0_eq$constraints)) { stop("equality constraints in x0 returns NA") } if (anyNA(g0_eq$jacobian)) { stop("jacobian of equality constraints in x0 returns NA") } if (length(g0_eq$jacobian) != length(g0_eq$constraints) * lx0) { stop("wrong number of elements in jacobian of equality ", "constraints (is ", length(g0_eq$jacobian), ", but should be ", length(g0_eq$constraints), " x ", lx0, " = ", length(g0_eq$constraints) * lx0, ")") } # check whether algorithm needs a derivative if (x$options$algorithm %in% list_algorithms_n) { warning("a gradient was supplied for the equality ", "constraints, but algorithm ", x$options$algorithm, " does not use gradients.") } } else { if (anyNA(g0_eq)) stop("equality constraints in x0 returns NA") # check whether algorithm needs a derivative if (x$options$algorithm %in% list_algorithms_d) { stop("A gradient for the equality constraints is needed by ", "algorithm ", x$options$algorithm, " but was not supplied.\n") } } } # check if we have a correct algorithm for the equality constraints if (x$num_constraints_eq > 0) { eq_algorithms <- c("NLOPT_LD_AUGLAG", "NLOPT_LN_AUGLAG", "NLOPT_LD_AUGLAG_EQ", "NLOPT_LN_AUGLAG_EQ", "NLOPT_GN_ISRES", "NLOPT_LD_SLSQP", "NLOPT_LN_COBYLA") if (!(x$options$algorithm %in% eq_algorithms)) { stop("If you want to use equality constraints, ", "then you should use one of these algorithms ", toString(eq_algorithms)) } } # check if a local optimizer was supplied, which is needed by some algorithms if (x$options$algorithm %in% c("NLOPT_LD_AUGLAG", "NLOPT_LN_AUGLAG", "NLOPT_LD_AUGLAG_EQ", "NLOPT_LN_AUGLAG_EQ", "NLOPT_GN_MLSL", "NLOPT_GD_MLSL", "NLOPT_GN_MLSL_LDS", "NLOPT_GD_MLSL_LDS") && is.null(x$local_options)) { stop("The algorithm ", x$options$algorithm, " needs a local ", "optimizer; specify an algorithm and termination condition in ", "local_opts") } # Check if the vector with tolerances for the inequality constraints is of # the same size as the number of constraints. if (x$num_constraints_ineq != length(x$options$tol_constraints_ineq)) { stop("The vector tol_constraints_ineq in the options list has size ", length(x$options$tol_constraints_ineq), " which is unequal to the number of inequality constraints, ", x$num_constraints_ineq, ".") } # Check if the vector with tolerances for the equality constraints is of the # same size as the number of constraints. if (x$num_constraints_eq != length(x$options$tol_constraints_eq)) { stop("The vector tol_constraints_eq in the options list has size ", length(x$options$tol_constraints_eq), " which is unequal to the number of equality constraints, ", x$num_constraints_eq, ".") } TRUE } nloptr/R/gradients.R0000644000176200001440000000506714472612401014105 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: gradients.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Functions to calculate numerical Gradient and Jacobian. # # CHANGELOG # # 2023-02-09: Cleanup and tweaks for safety and efficiency. Also Changed # nl.grad error message to be more mathematically precise. The loop # construct is 4 times faster than full vectorization with apply and # around 25% faster than partial vectorization creating a heps using # diag and pulling vectors off row-by-row in nl.grad & nl.jacobian. # (Avraham Adler) # #' Numerical Gradients and Jacobians #' #' Provides numerical gradients and Jacobians. #' #' Both functions apply the ``central difference formula'' with step size as #' recommended in the literature. #' #' @aliases nl.grad nl.jacobian #' #' @param x0 point as a vector where the gradient is to be calculated. #' @param fn scalar function of one or several variables. #' @param heps step size to be used. #' @param \dots additional arguments passed to the function. #' #' @return \code{grad} returns the gradient as a vector; \code{jacobian} #' returns the Jacobian as a matrix of usual dimensions. #' #' @export #' #' @author Hans W. Borchers #' #' @examples #' #' fn1 <- function(x) sum(x ^ 2) #' nl.grad(seq(0, 1, by = 0.2), fn1) #' ## [1] 0.0 0.4 0.8 1.2 1.6 2.0 #' nl.grad(rep(1, 5), fn1) #' ## [1] 2 2 2 2 2 #' #' fn2 <- function(x) c(sin(x), cos(x)) #' x <- (0:1) * 2 * pi #' nl.jacobian(x, fn2) #' ## [,1] [,2] #' ## [1,] 1 0 #' ## [2,] 0 1 #' ## [3,] 0 0 #' ## [4,] 0 0 #' nl.grad <- function(x0, fn, heps = .Machine$double.eps ^ (1 / 3), ...) { if (!is.numeric(x0)) stop("Argument 'x0' must be a numeric value.") fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (length(fn(x0)) != 1) stop("Function 'f' must be a scalar function (return a single value).") n <- length(x0) hh <- gr <- rep(0, n) for (i in seq_len(n)) { hh[i] <- heps gr[i] <- (fn(x0 + hh) - fn(x0 - hh)) / (2 * heps) hh[i] <- 0 } gr } #' @export nl.jacobian <- function(x0, fn, heps = .Machine$double.eps ^ (1 / 3), ...) { n <- length(x0) if (!is.numeric(x0) || n == 0) stop("Argument 'x' must be a non-empty numeric vector.") fun <- match.fun(fn) fn <- function(x) fun(x, ...) jacob <- matrix(NA_real_, length(fn(x0)), n) hh <- rep(0, n) for (i in seq_len(n)) { hh[i] <- heps jacob[, i] <- (fn(x0 + hh) - fn(x0 - hh)) / (2 * heps) hh[i] <- 0 } jacob } nloptr/R/mlsl.R0000644000176200001440000001300314633255630013067 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: mlsl.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Multi-Level Single-Linkage. # # CHANGELOG: # # 2014-05-05: Replaced cat by warning. # 2023-02-09: Cleanup and tweaks for safety and efficiency. (Avraham Adler) # Question, should passing a non-Gradient solver fail directly? It will # anyway. (Avraham Adler) # 2024-06-04: Cleaned up the Hartmann 6 example. (Avraham Adler) # #' Multi-level Single-linkage #' #' The \dQuote{Multi-Level Single-Linkage} (\acronym{MLSL}) algorithm for global #' optimization searches by a sequence of local optimizations from random #' starting points. A modification of \acronym{MLSL} is included using a #' low-discrepancy sequence (\acronym{LDS}) instead of pseudorandom numbers. #' #' \acronym{MLSL} is a \sQuote{multistart} algorithm: it works by doing a #' sequence of local optimizations---using some other local optimization #' algorithm---from random or low-discrepancy starting points. MLSL is #' distinguished, however, by a `clustering' heuristic that helps it to avoid #' repeated searches of the same local optima and also has some theoretical #' guarantees of finding all local optima in a finite number of local #' minimizations. #' #' The local-search portion of \acronym{MLSL} can use any of the other #' algorithms in \acronym{NLopt}, and, in particular, can use either #' gradient-based or derivative-free algorithms. For this wrapper only #' gradient-based \acronym{LBFGS} is available as local method. #' #' @param x0 initial point for searching the optimum. #' @param fn objective function that is to be minimized. #' @param gr gradient of function \code{fn}; will be calculated numerically if #' not specified. #' @param lower,upper lower and upper bound constraints. #' @param local.method only \code{BFGS} for the moment. #' @param low.discrepancy logical; shall a low discrepancy variation be used. #' @param nl.info logical; shall the original \acronym{NLopt} info be shown. #' @param control list of options, see \code{nl.opts} for help. #' @param ... additional arguments passed to the function. #' #' @return List with components: #' \item{par}{the optimal solution found so far.} #' \item{value}{the function value corresponding to \code{par}.} #' \item{iter}{number of (outer) iterations, see \code{maxeval}.} #' \item{convergence}{integer code indicating successful completion (> 0) #' or a possible error number (< 0).} #' \item{message}{character string produced by \acronym{NLopt} and giving #' additional information.} #' #' @export mlsl #' #' @author Hans W. Borchers #' #' @note If you don't set a stopping tolerance for your local-optimization #' algorithm, \acronym{MLSL} defaults to \code{ftol_rel = 1e-15} and #' \code{xtol_rel = 1e-7} for the local searches. #' #' @seealso \code{\link{direct}} #' #' @references A. H. G. Rinnooy Kan and G. T. Timmer, \dQuote{Stochastic global #' optimization methods} Mathematical Programming, vol. 39, p. 27-78 (1987). #' #' Sergei Kucherenko and Yury Sytsko, \dQuote{Application of deterministic #' low-discrepancy sequences in global optimization}, Computational #' Optimization and Applications, vol. 30, p. 297-318 (2005). #' #' @examples #' #' ## Minimize the Hartmann 6-Dimensional function #' ## See https://www.sfu.ca/~ssurjano/hart6.html #' #' a <- c(1.0, 1.2, 3.0, 3.2) #' A <- matrix(c(10, 0.05, 3, 17, #' 3, 10, 3.5, 8, #' 17, 17, 1.7, 0.05, #' 3.5, 0.1, 10, 10, #' 1.7, 8, 17, 0.1, #' 8, 14, 8, 14), nrow = 4) #' #' B <- matrix(c(.1312, .2329, .2348, .4047, #' .1696, .4135, .1451, .8828, #' .5569, .8307, .3522, .8732, #' .0124, .3736, .2883, .5743, #' .8283, .1004, .3047, .1091, #' .5886, .9991, .6650, .0381), nrow = 4) #' #' hartmann6 <- function(x, a, A, B) { #' fun <- 0 #' for (i in 1:4) { #' fun <- fun - a[i] * exp(-sum(A[i, ] * (x - B[i, ]) ^ 2)) #' } #' #' fun #' } #' #' ## The function has a global minimum of -3.32237 at #' ## (0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573) #' #' S <- mlsl(x0 = rep(0, 6), hartmann6, lower = rep(0, 6), upper = rep(1, 6), #' nl.info = TRUE, control = list(xtol_rel = 1e-8, maxeval = 1000), #' a = a, A = A, B = B) #' mlsl <- function(x0, fn, gr = NULL, lower, upper, local.method = "LBFGS", low.discrepancy = TRUE, nl.info = FALSE, control = list(), ...) { local_opts <- list(algorithm = "NLOPT_LD_LBFGS", xtol_rel = 1e-4) opts <- nl.opts(control) if (low.discrepancy) { opts["algorithm"] <- "NLOPT_GD_MLSL_LDS" } else { opts["algorithm"] <- "NLOPT_GD_MLSL" } opts[["local_opts"]] <- local_opts fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (local.method == "LBFGS") { if (is.null(gr)) { gr <- function(x) nl.grad(x, fn) } else { .gr <- match.fun(gr) gr <- function(x) .gr(x, ...) } } else { warning("Only gradient-based LBFGS available as local method. ", "To use another method please use the nloptr interface.") gr <- NULL } S0 <- nloptr(x0 = x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) } nloptr/R/check.derivatives.R0000644000176200001440000001522014472612401015516 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: check.derivatives.R # Author: Jelmer Ypma # Date: 24 July 2011 # # Compare analytic derivatives wih finite difference approximations. # # Input: # .x : compare at this point # func : calculate finite difference approximation for the gradient of # this function # func_grad : function to calculate analytic gradients # check_derivatives_tol : show deviations larger than this value # (optional) # check_derivatives_print : print the values of the function (optional) # func_grad_name : name of function to show in output (optional) # ... : arguments that are passed to the user-defined function (func and # func_grad) # # Output: list with analytic gradients, finite difference approximations, # relative errors and a comparison of the relative errors to the # tolerance. # # CHANGELOG: # 2013-10-27: Added relative_error and flag_derivative_warning to output list. # 2014-05-05: Replaced cat by message, so messages can now be suppressed by # suppressMessages. # 2023-02-09: Cleanup and tweaks for safety and efficiency (AA) #' Check analytic gradients of a function using finite difference #' approximations #' #' This function compares the analytic gradients of a function with a finite #' difference approximation and prints the results of these checks. #' #' @param .x point at which the comparison is done. #' @param func function to be evaluated. #' @param func_grad function calculating the analytic gradients. #' @param check_derivatives_tol option determining when differences between the #' analytic gradient and its finite difference approximation are flagged as an #' error. #' @param check_derivatives_print option related to the amount of output. 'all' #' means that all comparisons are shown, 'errors' only shows comparisons that #' are flagged as an error, and 'none' shows the number of errors only. #' @param func_grad_name option to change the name of the gradient function #' that shows up in the output. #' @param ... further arguments passed to the functions func and func_grad. #' #' @return The return value contains a list with the analytic gradient, its #' finite difference approximation, the relative errors, and vector comparing #' the relative errors to the tolerance. #' #' @export #' #' @author Jelmer Ypma #' #' @seealso \code{\link[nloptr:nloptr]{nloptr}} #' #' @keywords optimize interface #' #' @examples #' #' library('nloptr') #' #' # example with correct gradient #' f <- function(x, a) sum((x - a) ^ 2) #' #' f_grad <- function(x, a) 2 * (x - a) #' #' check.derivatives(.x = 1:10, func = f, func_grad = f_grad, #' check_derivatives_print = 'none', a = runif(10)) #' #' # example with incorrect gradient #' f_grad <- function(x, a) 2 * (x - a) + c(0, 0.1, rep(0, 8)) #' #' check.derivatives(.x = 1:10, func = f, func_grad = f_grad, #' check_derivatives_print = 'errors', a = runif(10)) #' #' # example with incorrect gradient of vector-valued function #' g <- function(x, a) c(sum(x - a), sum((x - a) ^ 2)) #' #' g_grad <- function(x, a) { #' rbind(rep(1, length(x)) + c(0, 0.01, rep(0, 8)), #' 2 * (x - a) + c(0, 0.1, rep(0, 8))) #' } #' #' check.derivatives(.x = 1:10, func = g, func_grad = g_grad, #' check_derivatives_print = 'all', a = runif(10)) #' check.derivatives <- function(.x, func, func_grad, check_derivatives_tol = 1e-04, check_derivatives_print = "all", func_grad_name = "grad_f", ...) { analytic_grad <- func_grad(.x, ...) finite_diff_grad <- finite.diff(func, .x, ...) relative_error <- ifelse(finite_diff_grad == 0, analytic_grad, abs((analytic_grad - finite_diff_grad) / finite_diff_grad)) flag_derivative_warning <- relative_error > check_derivatives_tol if (!(check_derivatives_print %in% c("all", "errors", "none"))) { warning("Value '", check_derivatives_print, "' for check_derivatives_print is unknown; use 'all' ", "(default), 'errors', or 'none'.") check_derivatives_print <- "none" } # determine indices of vector / matrix for printing # format indices with width, such that they are aligned vertically if (is.matrix(analytic_grad)) { indices <- paste(format(rep(seq_len(nrow(analytic_grad)), times = ncol(analytic_grad)), width = 1 + sum(nrow(analytic_grad) > 10 ^ (1:10))), format(rep(seq_len(ncol(analytic_grad)), each = nrow(analytic_grad)), width = 1 + sum(ncol(analytic_grad) > 10 ^ (1:10))), sep = ", ") } else { indices <- format(seq_along(analytic_grad), width = 1 + sum(length(analytic_grad)) > 10 ^ (1:10)) } # Print results. message("Derivative checker results: ", sum(flag_derivative_warning), " error(s) detected.") if (check_derivatives_print == "all") { message("\n", paste0(ifelse(flag_derivative_warning, "*", " "), " ", func_grad_name, "[", indices, "] = ", format(analytic_grad, scientific = TRUE), " ~ ", format(finite_diff_grad, scientific = TRUE), " [", format(relative_error, scientific = TRUE), "]", collapse = "\n"), "\n\n") } else if (check_derivatives_print == "errors") { if (sum(flag_derivative_warning) > 0) { message("\n", paste0(ifelse(flag_derivative_warning[flag_derivative_warning], "*", " "), " ", func_grad_name, "[", indices[flag_derivative_warning], "] = ", format(analytic_grad[flag_derivative_warning], scientific = TRUE), " ~ ", format(finite_diff_grad[flag_derivative_warning], scientific = TRUE), " [", format(relative_error[flag_derivative_warning], scientific = TRUE), "]", collapse = "\n"), "\n\n") } } else if (check_derivatives_print == "none") {} list("analytic" = analytic_grad, "finite_difference" = finite_diff_grad, "relative_error" = relative_error, "flag_derivative_warning" = flag_derivative_warning) } nloptr/cleanup0000755000176200001440000000014314765523732013161 0ustar liggesusers#! /bin/sh rm -fr src/nlopt src/Makevars src/*.o src/*.so autom4te.cache config.log config.status nloptr/vignettes/0000755000176200001440000000000014765523731013615 5ustar liggesusersnloptr/vignettes/nloptr.Rmd0000644000176200001440000003406314613776363015610 0ustar liggesusers--- title: "nloptr" author: "Jelmer Ypma, Aymeric Stamm, and Avraham Adler" date: "`r Sys.Date()`" output: rmarkdown::html_vignette bibliography: reflist.bib nocite: | @NLopt:website vignette: > %\VignetteIndexEntry{nloptr} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r setSweaveOptions,echo=FALSE} # have an (invisible) initialization noweb chunk # to remove the default continuation prompt ">" options(continue = " ") options(width = 60) # eliminate margin space above plots options(SweaveHooks = list(fig = function() par(mar = c(5.1, 4.1, 1.1, 2.1)))) ``` This document is an introduction to `nloptr`: an R interface to NLopt. [NLopt](https://nlopt.readthedocs.io/en/latest/) is a free/open-source library for nonlinear optimization, started by Steven G. Johnson, providing a common interface for a number of different free optimization routines available online as well as original implementations of various other algorithms. The NLopt library is available under the GNU Lesser General Public License (LGPL), and the copyrights are owned by a variety of authors. This package should be considered in beta and comments about any aspect of the package are welcome. This document is an R vignette prepared with the aid of `knitr` [@Xie:2014; @Xie:2015; @Xie:2016]. Financial support of the UK Economic and Social Research Council through a grant (RES-589-28-0001) to the ESRC Centre for Microdata Methods and Practice (CeMMAP) is gratefully acknowledged. ## Introduction NLopt addresses general nonlinear optimization problems of the form: $$ \begin{aligned} &\min_{x \in R^n} f(x) \\ s.t.& g(x) \leq 0 \\ & h(x) = 0 \\ & x_L \leq x \leq x_U \end{aligned} $$ where $f(\cdot)$ is the objective function and $x$ represents the $n$ optimization parameters. This problem may optionally be subject to the bound constraints (also called box constraints), $x_L$ and $x_U$. For partially or totally unconstrained problems the bounds can take values $-\infty$ or $\infty$. One may also optionally have $m$ nonlinear inequality constraints---sometimes called a nonlinear programming problem---which may be specified in $g(\cdot)$, and equality constraints which may be specified in $h(\cdot)$. Note that not all of the algorithms in NLopt can handle constraints. This vignette describes how to formulate minimization problems to be solved with the R interface to NLopt. If you want to use the C interface directly or are interested in the Matlab interface, there are other sources of documentation available. Some of the information here has been taken from the NLopt website, where more details are available. All credit for implementing the C code for the different algorithms available in NLopt should go to the respective authors. Also, please see the [website](https://nlopt.readthedocs.io/en/latest/Citing_NLopt/) for information on how to cite NLopt and the algorithms you use. ## Installation This package is on CRAN and can be installed from within R using ```{r installNLopt, eval=FALSE} install.packages("nloptr") ``` or ```{r installNLoptSource, eval=FALSE} install.packages("nloptr", type = "source") ``` to install the package from source. You should now be able to load the R interface to NLopt and read the help. ```{r testNLoptInstallation, eval=FALSE} library("nloptr") ?nloptr ``` The most recent experimental *source* version of `nloptr` can be installed from Github using the `remotes` package: ```{r installNLoptGithub, eval=FALSE} # install.packages("remotes") remotes::install_github("astamm/nloptr") ``` ## Minimizing the Rosenbrock Banana function As a first example we will solve an unconstrained minimization problem. The function we look at is the Rosenbrock Banana function: $$ f(x) = 100 \left(x_2-x_1^2\right)^2 + \left(1-x_1\right)^2, $$ which is also used as an example in the documentation for the standard R optimizer `optim`. The gradient of the objective function is given by: $$ \nabla f(x) = \left(\begin{array}[1]{c} -400 \cdot x_1 \cdot (x_2 - x_1^2) - 2 \cdot (1 - x_1) \\ 200 \cdot (x_2 - x_1^2) \end{array} \right). $$ Not all of the algorithms in NLopt need gradients to be supplied by the user. We will show examples with and without supplying the gradient. After loading the library. ```{r loadLibrary} library(nloptr) ``` We start by specifying the objective function and its gradient: ```{r defineRosenbrockBanana} ## Rosenbrock Banana function eval_f <- function(x) { 100 * (x[2] - x[1] * x[1]) ^ 2 + (1 - x[1]) ^ 2 } ## Gradient of Rosenbrock Banana function eval_grad_f <- function(x) { c(-400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), 200 * (x[2] - x[1] * x[1])) } ``` We define initial values ```{r setRosenbrockBananaInitialValues} # initial values x0 <- c(-1.2, 1) ``` and then minimize the function using the `nloptr` command. This command runs some checks on the supplied inputs and returns an object with the exit code of the solver, the optimal value of the objective function and the solution. Before we can minimize the function we need to specify which algorithm we want to use ```{r setRosenbrockBananaOptions} opts <- list("algorithm" = "NLOPT_LD_LBFGS", "xtol_rel" = 1.0e-8) ``` Here we use the L-BFGS algorithm [@Nocedal:1980; @LiuNocedal:1989]. The characters `LD` in the algorithm show that this algorithm looks for local minima (`L`) using a derivative-based (`D`) algorithm. Other algorithms look for global (`G`) minima, or they don't need derivatives (`N`). We also specified the termination criterium in terms of the relative x-tolerance. Other termination criteria are available (see Appendix `\ref{sec:descoptions}` for a full list of options). We then solve the minimization problem using ```{r solveRosenbrockBanana} # solve Rosenbrock Banana function res <- nloptr(x0 = x0, eval_f = eval_f, eval_grad_f = eval_grad_f, opts = opts) ``` We can see the results by printing the resulting object. ```{r printRosenbrockBanana} print(res) ``` Sometimes the objective function and its gradient contain common terms. To economize on calculations, we can return the objective and its gradient in a list. For the Rosenbrock Banana function we have for instance: ```{r defineRosenbrockBananaList} ## Rosenbrock Banana function and gradient in one function eval_f_list <- function(x) { common_term <- x[2] - x[1] * x[1] list("objective" = 100 * common_term ^ 2 + (1 - x[1]) ^ 2, "gradient" = c(-400 * x[1] * common_term - 2 * (1 - x[1]), 200 * common_term)) } ``` which we minimize using ```{r solveRosenbrockBananaList} res <- nloptr(x0 = x0, eval_f = eval_f_list, opts = opts) print(res) ``` This gives the same results as before. ## Minimization with inequality constraints This section shows how to minimize a function subject to inequality constraints. This example is the same as the one used in the tutorial on the NLopt website. The problem we want to solve is: $$ \begin{aligned} &\min_{x \in R^n} \sqrt{x_2} \\ s.t.& x_2 \geq 0 \\ & x_2 \geq (a_1 x_1 + b_1)^3 \\ & x_2 \geq (a_2 x_1 + b_2)^3, \end{aligned} $$ where $a_1 = 2$, $b_1 = 0$, $a_2 = -1$, and $b_2 = 1$. In order to solve this problem, we first have to re-formulate the constraints to be of the form $g(x) \leq 0$. Note that the first constraint is a bound on $x_2$, which we will add later. The other two constraints can be re-written as: $$ \begin{aligned} (a_1 x_1 + b_1)^3 - x_2 &\leq 0 \\ (a_2 x_1 + b_2)^3 - x_2 &\leq 0 \end{aligned} $$ First, define R functions to calculate the objective function and its gradient: ```{r defineTutorialObjective} # objective function eval_f0 <- function(x, a, b) { sqrt(x[2]) } # gradient of objective function eval_grad_f0 <- function(x, a, b) { c(0, 0.5 / sqrt(x[2])) } ``` If needed, these can of course be calculated in the same function as before. Then define the two constraints and the Jacobian of the constraints: ```{r defineTutorialConstraints} # constraint function eval_g0 <- function(x, a, b) { (a * x[1] + b) ^ 3 - x[2] } # Jacobian of constraint eval_jac_g0 <- function(x, a, b) { rbind(c(3 * a[1] * (a[1] * x[1] + b[1]) ^ 2, -1.0), c(3 * a[2] * (a[2] * x[1] + b[2]) ^ 2, -1.0)) } ``` Note that all of the functions above depend on additional parameters, `a` and `b`. We have to supply specific values for these when we invoke the optimization command. The constraint function `eval_g0` returns a vector with in this case the same length as the vectors `a` and `b`. The function calculating the Jacobian of the constraint should return a matrix where the number of rows equal the number of constraints (in this case two). The number of columns should equal the number of control variables (two in this case as well). After defining values for the parameters ```{r defineTutorialParameters} # define parameters a <- c(2, -1) b <- c(0, 1) ``` we can minimize the function subject to the constraints with the following command: ```{r solveTutorialWithGradient} # Solve using NLOPT_LD_MMA with gradient information supplied in separate # function res0 <- nloptr(x0 = c(1.234, 5.678), eval_f = eval_f0, eval_grad_f = eval_grad_f0, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g0, eval_jac_g_ineq = eval_jac_g0, opts = list("algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1.0e-8, "print_level" = 2, "check_derivatives" = TRUE, "check_derivatives_print" = "all"), a = a, b = b) print(res0) ``` Here we supplied lower bounds for $x_2$ in `lb`. There are no upper bounds for both control variables, so we supply `Inf` values. If we don't supply lower or upper bounds, plus or minus infinity is chosen by default. The inequality constraints and its Jacobian are defined using `eval_g_ineq` and `eval_jac_g_ineq`. Not all algorithms can handle inequality constraints, so we have to specify one that does, `NLOPT_LD_MMA` [@Svanberg:2002]. We also specify the option `print_level` to obtain output during the optimization process. For the available `print_level` values, see `?nloptr`. Setting the `check_derivatives` option to `TRUE`, compares the gradients supplied by the user with a finite difference approximation in the initial point (`x0`). When this check is run, the option `check_derivatives_print` can be used to print all values of the derivative checker (`all` (default)), only those values that result in an error (`errors`) or no output (`none`), in which case only the number of errors is shown. The tolerance that determines if a difference between the analytic gradient and the finite difference approximation results in an error can be set using the option `check_derivatives_tol` (default = 1e-04). The first column shows the value of the analytic gradient, the second column shows the value of the finite difference approximation, and the third column shows the relative error. Stars are added at the front of a line if the relative error is larger than the specified tolerance. Finally, we add all the parameters that have to be passed on to the objective and constraint functions, `a` and `b`. We can also use a different algorithm to solve the same minimization problem. The only thing we have to change is the algorithm that we want to use, in this case `NLOPT_LN_COBYLA`, which is an algorithm that doesn't need gradient information [@Powell:1994; @Powell:1998]. ```{r solveTutorialWithoutGradient} # Solve using NLOPT_LN_COBYLA without gradient information res1 <- nloptr(x0 = c(1.234, 5.678), eval_f = eval_f0, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g0, opts = list("algorithm" = "NLOPT_LN_COBYLA", "xtol_rel" = 1.0e-8), a = a, b = b) print(res1) ``` ## Derivative checker The derivative checker can be called when supplying a minimization problem to `nloptr`, using the options `check_derivatives`, `check_derivatives_tol` and `check_derivatives_print`, but it can also be used separately. For example, define the function `g`, with vector outcome, and its gradient `g_grad`: ```{r derivativeCheckerDefineFunctions} g <- function(x, a) { c(x[1] - a[1], x[2] - a[2], (x[1] - a[1]) ^ 2, (x[2] - a[2]) ^ 2, (x[1] - a[1]) ^ 3, (x[2] - a[2]) ^ 3) } g_grad <- function(x, a) { rbind( c(1, 0), c(0, 1), c(2 * (x[1] - a[1]), 0), c(2 * (x[1] - a[1]), 2 * (x[2] - a[2])), c(3 * (x[1] - a[2]) ^ 2, 0), c(0, 3 * (x[2] - a[2]) ^ 2) ) } ``` `a` is some vector containing data. The gradient contains some errors in this case. By calling the function `check.derivatives` we can check the user-supplied analytic gradients with a finite difference approximation at a point `.x`. ```{r derivativeCheckerPrint} res <- check.derivatives( .x = c(1, 2), func = g, func_grad = g_grad, check_derivatives_print = "all", a = c(0.3, 0.8) ) ``` The errors are shown on screen, where the option `check_derivatives_print` determines the amount of output you see. The value of the analytic gradient and the value of the finite difference approximation at the supplied point is returned in a list. ```{r derivativeCheckerResult} res ``` Note that not all errors will be picked up by the derivative checker. For instance, if we run the check with `a = c(.5, .5)`, one of the errors is not flagged as an error. ## Notes The `.R` scripts in the `tests` directory contain more examples. For instance, `hs071.R` and `systemofeq.R` show how to solve problems with equality constraints. See the [NLopt website](https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#augmented-lagrangian-algorithm) for more details. Please let us know if there are any of features implemented in NLopt which should be implemented in `nloptr`. Sometimes the optimization procedure terminates with a message `maxtime was reached` without evaluating the objective function. Submitting the same problem again usually solves this problem. ## Description of options ```{r printAllOptions} nloptr::nloptr.print.options() ``` ## References nloptr/vignettes/reflist.bib0000644000176200001440000000454514613534462015746 0ustar liggesusers@MISC{NLopt:website, author = {Steven G. Johnson}, title = {The {N}{L}opt nonlinear-optimization package}, url = {https://nlopt.readthedocs.io/en/latest/} } @inproceedings{Powell:1994, author = {M. J. D. Powell}, title = {A direct search optimization method that models the objective and constraint functions by linear interpolation}, booktitle = {Advances in Optimization and Numerical Analysis}, editor = {S. Gomez and J.-P. Hennart}, publisher = {Kluwer Academic, Dordrecht}, pages = {51--67}, year = {1994} } @article{Powell:1998, author = {M. J. D. Powell}, title = {Direct search algorithms for optimization calculations}, journal = {Acta Numerica}, volume = {7}, pages = {287--336}, year = {1998} } @article{Svanberg:2002, author = {Krister Svanberg}, title = {A class of globally convergent optimization methods based on conservative convex separable approximations}, journal = {SIAM J. Optim.}, volume = {12}, number = {2}, pages = {555--573}, year = {2002} } @article{LiuNocedal:1989, author = {D. C. Liu and J. Nocedal}, title = {On the limited memory {B}{F}{G}{S} method for large scale optimization}, journal = {Math. Programming}, volume = {45}, pages = {503--528}, year = {1989} } @article{Nocedal:1980, author = {J. Nocedal}, title = {Updating quasi-{N}ewton matrices with limited storage}, journal = {Math. Comput.}, volume = {35}, pages = {773--782}, year = {1980} } @Manual{Xie:2016, title = {knitr: A General-Purpose Package for Dynamic Report Generation in R}, author = {Yihui Xie}, year = {2016}, note = {R package version 1.14}, url = {https://yihui.org/knitr/}, } @Book{Xie:2015, title = {Dynamic Documents with {R} and knitr}, author = {Yihui Xie}, publisher = {Chapman and Hall/CRC}, address = {Boca Raton, Florida}, year = {2015}, edition = {2nd}, note = {ISBN 978-1498716963}, url = {https://yihui.org/knitr/}, } @InCollection{Xie:2014, booktitle = {Implementing Reproducible Computational Research}, editor = {Victoria Stodden and Friedrich Leisch and Roger D. Peng}, title = {knitr: A Comprehensive Tool for Reproducible Research in {R}}, author = {Yihui Xie}, publisher = {Chapman and Hall/CRC}, year = {2014}, note = {ISBN 978-1466561595}, url = {https://www.routledge.com/Implementing-Reproducible-Research/Stodden-Leisch-Peng/p/book/9781466561595}, } nloptr/src/0000755000176200001440000000000014765523731012374 5ustar liggesusersnloptr/src/nlopt-src.tar.gz0000644000176200001440000770117514765070675015472 0ustar liggesusers\k{Ȓ~2Ko~6{cl` xvHmXR&^oUyN!FUVUލP{,<|+kq:^kfu *s_Ot/KR']#׿Q4%C ?Y,0}\32B (e=g !&ZpAg!H"BuH3>D!}P̨1Yf"k3TMm d`30b-t@.r;{OL#̩-oDg0Џؾ5qF_әXP j"p\`<{jY]Ps ["<&ڝ>toBw815Ι@|YDždE@N<,ED`T(%Mxp'Yxw<JpX,p7p1v?}J:#굢"b,͈D^j8ȽuS% %=Fwsj=D 8"MXurar0Do5"<%LZ4q '^7ceR0ǥeYo'gp麦!чHLθ{K=' QɃB76d_w>!ImB?y!Z1WVWǵ@9d`v@ȶHk,+AL$GNY 4lM"74 c*6jJK yeS#95Bz,A(ꔅ$,K%_Ob@TP,6v#[)ô^τB4)ed %ӿM(lvרi֓LlZ hoUpF4  _0pw$bRgmURҎ筷qz`9^^/zh|M:5^Ђzm6DEݐPg<+d/R(4{D{ރ) f׫M'ﻧv|uvϴT"G.iiABR"dvÙmiUGm=#I| D-7ZE!v FD[!CJH MQ=j뤊N/TQ^ս`_󺞗ɇBrz z-\S0w) aȲ?/&>[l,Tw > rBv(4\>f\Mpk, |:j뀇 ˼S\ewսODhy/]-Rv- Eà oiTߺ_34zO*?bG-h@ϧXÐ+.s9#dsS37.@}ڑ;<ԙ{.I ]Ձ:#o"CW9%@F]Km<~&FnDnDx05ta8 CpJjuS8y5釼Tԧ brȜ&PYF@>u6bԈ+\H?-'>m9GXD]@)owGQO oJ\azt]܄ *MWH{`G!mF^TSū]גNbXa;e&p6%Z <. fbEChȷ?i«Un=+, M$53)]`40(\ֲ.u &H[k2Z!M-M\ȀS-kZVyygu9nX>q, `V~H!9^?Πəd5+0SVv*iX,Ō5C7PS>/ Vqp;Fa"IO3,}6Lx @ fC's%(̋Yigp btFu}*&Rh,y fc+^u"}H-raIZ%;gw,}2+ IfB&W;E`9 _.)7 Uj*Sk[Br~z Z1e(`kx2d AGЇ 0D]>]y> aQ)6cN,jhrV{ﻝNgEF@YAD`6xp(^N2Jhm2֐9[vY c)6MܛP@7L=&\hţ^3(Zܞÿ@f֦-r\CN8e.\S_jEyϢ =]\}N4bb pW*TR)#b!J].|[09s-Kc1rD#ewkeʎhώ| Z=+657aFA9=ar]oT$$fE+6VWUci.jZM8xǵ&akyk`v`w* RL =2+C{@ۚST">ZO@ˀ" AVDy=uSEFU&Ȝa @eٔ_I>&>jY> M輿>JZmr. $VnԵ2gU8.n1ysT7"Ht6ROh}=܁ 8Cv@}Q`غi Gw!!IY\=h7Cb8SwY30`[3KA$ԑ^; ;b f[~$~Z l@8X>թd`Tf9kzE/>e}=R▯GnKG #|%of G^*)4*l 괈׵I4 D! . =$슀͙6&\ 3 ՃwIjE@SnJqRlR5JGvhAqRAH6~<3zfen4U$XiI|Ȏ7t%tL ُQRXOp"ȳIqĺrjoʩψ}EɩARH%td8ITa*I.60XVⱝf1~ nfdjj 5#pE6s1=fD$|܆hDCbazppx]VdJL,Ũk 3.}=4JPz2E$Mcc H*Z*r IxC=VJ:ٷȀVH+${I;ͶS:LٺI8dGBD}:$uTHk;ݛyy 4To Sh T+n;= 7-M,Vb<=^=< -7ROVV4wwa4A=^<6z#;fB ?2fݻ<1hLxA[V:^/{6w 3U'Ȳ%gvI9kE9go%ֆQaK dgJ, n4jv-o9hf5Se\w0b>B 낇/wֱP&iֳպ ι݄7F MYub ` AmY XazU6o]DXUcb|'DA=\|uNsESk7ŧPl]VLunGZqTǓ-L V"M$4P~N@pu'W*{~v{06)8B:M[*_Au+XomްvN>6;M<ԑ wH)(Fn@ }9qָ`5Vy;=h兌1,*j7sa;z^#jt&=IM?Y0U"bҹvDY8쪞 X l$4'\²Ɇs`2c%|dLt^O[? _WjWP)[l%d^+ `娐C%5ÉfL,1n ij=}6ԗ@6.vDupo.0"; H ٤:b4 +vj6֍[+Q8Nory dfL9+ xeg}1W*𐘮p4vz?]oCP֕ mE|U+O (4 r>t9# ,(7JtJGWw`a 5at<^*Q)~~ى⸔s̭xna۠B p颟Ei1zRO[Ӻ@}O0=W䨾;aS DALPi5Ǫˮf8c$`9.nrPX%?C?C}="'PCJ4,\%ۦ,1۽MFv7Xۣł@m 2hH/ܞ-!2BA&&1 qo+Ҏ#}SI%1*J蔧)wt)ɝBHCFg%.5oHA# 41f(~i-%կ֕ҚPPGJHI TSxzq7+}G-EQӇqRkbFɫqD@ Aweg/IR^w_d; 6wVZa[  ta;խ;n7I8= .t[xkX|>caDg\k .p)GVlR7YPc!HjKaٵ(gxgЯlL>äld=!SlNQ.2ýXkdԱb{2Yl+O&f.My <]esO@?&@:#j5 uT_?n+YJNN9ג"5NBO]SHEý+w Tnȕ$>S @t{kQvz77ю:BM-n;P5[JTTg=1c2vd>Qkut-, /h|g=ݫM=!w<s%k參1M6E3t6[-Uٵ0l >1AˌUzAZ|ni{I^[w#0kىŒNc`Gv6)j^5u {n= _{vG}Kj[v0pM:>s" 绸`:_;\Dɔ42{,nJ(NEpA: oۢn`r [~!Ӊ<"q~:Eãsh 6ĈнT!~vWwyp} 1q?B)w[@| qN7܂cA"6.F$] .BN+g  Aq3rTCԊ-R+F>dYf"[yHF y+Z) hːw5iA7nhȴVq`ؙyKG}t6H>PW~HHZ>tG;cqЍ u@,ju믿Jw eURaCxP V2ƙd)G!83|^9M/+Fu˶^Vy58d1T+ I5Kd3uD&gU.W]T oaBg7RM_*Tf~0$P (VSp5nƒr^-]W)omRR)|u(Rt%%eZ9XPs^$^MW+Ga+Oǔ0${PfKT.aׅfe;i&w~_.LT;o>DO:Goyxn_ k;#%Nx%TӒ[mPGɛbyqv8"coU, wן<:/gaȖG?@eɍ*j4Lv0H*N 7vE 0lǩ#l;,`4 rr)  ( w$2N>bMSCaĆƠ!s( sRu( =q"U/ 4)@0l Zn`d@ S~=a*i G 3L6_6BEt8Bu^Bg(J.R B mk4TԮned Ă* cY] `=~Ct L\㢌6e|j: j5 Ɛ-" <єyAp*E]Za g Pǔk7d_!EtY2wO+{87ہ`8KRŽ97ء+ETÖ@M9ߥ˨F NP0<̘ hrcrF`LQpԚ+)=ZXT<<u䴸=²Ѭj4¬, vaE뙲ؿ+ 4٥<.G]͠Bw )0ĉ{\T}QŽꑯEo/~*ar Fe ލ\Q8tCn|IPv%r(B˕]_TK SD{ȟdtlP!Stg(ʰ%쾋 eUZN[o6jK3i]Q/˦- ~xy䍅XRrH7,Gx;+{ ݭnp[! 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C*Ɗ(M'B-`0!hg8fq! @NH0@1~s5Evu>;C`E{ 0t"PT9|ZJ6pنr2J*[|(F/< 7Ɯ@gȵc.-;;y};O|V|hW$ _r[3?q؞ =RYjz8=?͌o3:f'$Ī;%&a;@Tpo凚@\s: M>3gHZD+p5q&gh&-?)WCj8"1%4ظVClvݮcuXWr<٥sּ#%35iJ-"4S>1Lafx9Zɥע BL#8 >i"hDM.G+ ^*DPЌ@ͮ`'=ceK-]Gtf#3n y ּESXD%J4e5>kN4J_ R=1;u)v[Y_E(7L 39hD)T4fdJW?~޼ 54& )~Q WYDꙐLgW1!-X,a#h g{.ŧʐM2ˊLH^نT*1 ⋕u 槤VrfkXL9l%8F,s"D93Rwl$J]G˪wc)Yq\:NQy4 m %(5:5GE\%ׄ4- èf!Zl4p,­ꙟ@ՍVcaXqz :e3cA'+  բ)lbGjhdqA8 &ڴA*.4 o—~h&6BR^+pS`hFr!OAq4M@)tf`-:36|A?ĭ)7gw<TQVyⵈz_Fb9bS ֘lje'h|h"H{؁~mWl!!/Rl%~'wNO._~ݔi'g'Rh <0ټe^Z,T.k#m63T:K8O:Eq22Vn1;h1>-n?32$+^$fK՗dy2U[\Umbn{/ tu5`O/>HdaɄh8W̥`yJbC} Й$tbhCSɧB3g_|^[rްvɦ`"V1gZj=ߟ>؆y -sopr¤ dR9S#(8 26um%PaJkpuH5Xx)XG7z\M6^QQtA%|'yCKk)hLQv7e;!Z}!v{Oϰ쥅hmk~]Wao4 q9;"rv\rч> V ؏6pKĪrIg(6#Fzm9*gs~^JrK8/tn01bN$?e6` qJX m >f&ʫVvxE-Y^oNcSNdp:)|5mm9lV/@?o Ɓ##(V'H97B԰ $<,3z>[-:҇!F^ oa eWƔ̭Rwin+ܮ `w\ADY/AܳpE}p @zպyX@#eːkt!mPfmv%Lu-x-fB Ridhn󧂕s6#q$NW0FC+y6ԀLcJC$x"KŅ; vn;ٝ}mn8*iA`䉚Ou*I 7.Ξ)\ƮѻN˫cĚ2px~y^vq8&P2qA$R %#DR6'C>Km?ţ<3Ux4N7\A#BM/R8L mS]J_rKDNKo֦J^ ;<8=XPf+pp YPFd֗f9nί\DQ=qM{D"~č|_y(O4=4^E\9QfYᚶz[V.+uV'y'dJ*^%el e80R 2KgKT.fm"B׾b=.(~. * * File: init_nloptr.c * Author: Jelmer Ypma * Date: 3 October 2017 * * This file registers C functions to be used from R. * * CHANGELOG: * 2017-10-01: Initial version. * 2017-10-03: Included registering of C functions to be used by external R * packages. * 2023-02-07: Use "modern" method for invoking native routine registration * (Avraham Adler). * 2023-08-24: Delete files solely needed for testthat (Avraham Adler). * 2024-07-02: Updated old include which is no longer maintained and other * minor code tweaks and efficiency enhancements (Avraham Adler). */ #include #include #include // for NULL #include #include "nloptr.h" #include static const R_CallMethodDef CallEntries[] = { {"NLoptR_Optimize", (DL_FUNC) &NLoptR_Optimize, 1}, {NULL, NULL, 0} }; void R_init_nloptr(DllInfo *info) { // Register C functions that can be used by external packages // linking to internal NLopt code from C. R_RegisterCCallable("nloptr", "nlopt_algorithm_name", (DL_FUNC) &nlopt_algorithm_name); R_RegisterCCallable("nloptr", "nlopt_srand", (DL_FUNC) &nlopt_srand); R_RegisterCCallable("nloptr", "nlopt_srand_time", (DL_FUNC) &nlopt_srand_time); R_RegisterCCallable("nloptr", "nlopt_version", (DL_FUNC) &nlopt_version); R_RegisterCCallable("nloptr", "nlopt_create", (DL_FUNC) &nlopt_create); R_RegisterCCallable("nloptr", "nlopt_destroy", (DL_FUNC) &nlopt_destroy); R_RegisterCCallable("nloptr", "nlopt_copy", (DL_FUNC) &nlopt_copy); R_RegisterCCallable("nloptr", "nlopt_optimize", (DL_FUNC) &nlopt_optimize); R_RegisterCCallable("nloptr", "nlopt_set_min_objective", (DL_FUNC) &nlopt_set_min_objective); R_RegisterCCallable("nloptr", "nlopt_set_max_objective", (DL_FUNC) &nlopt_set_max_objective); R_RegisterCCallable("nloptr", "nlopt_set_precond_min_objective", (DL_FUNC) &nlopt_set_precond_min_objective); R_RegisterCCallable("nloptr", "nlopt_set_precond_max_objective", (DL_FUNC) &nlopt_set_precond_max_objective); R_RegisterCCallable("nloptr", "nlopt_get_algorithm", (DL_FUNC) &nlopt_get_algorithm); R_RegisterCCallable("nloptr", "nlopt_get_dimension", (DL_FUNC) &nlopt_get_dimension); R_RegisterCCallable("nloptr", "nlopt_set_lower_bounds", (DL_FUNC) &nlopt_set_lower_bounds); R_RegisterCCallable("nloptr", "nlopt_set_lower_bounds1", (DL_FUNC) &nlopt_set_lower_bounds1); R_RegisterCCallable("nloptr", "nlopt_get_lower_bounds", (DL_FUNC) &nlopt_get_lower_bounds); R_RegisterCCallable("nloptr", "nlopt_set_upper_bounds", (DL_FUNC) &nlopt_set_upper_bounds); R_RegisterCCallable("nloptr", "nlopt_set_upper_bounds1", (DL_FUNC) &nlopt_set_upper_bounds1); R_RegisterCCallable("nloptr", "nlopt_get_upper_bounds", (DL_FUNC) &nlopt_get_upper_bounds); R_RegisterCCallable("nloptr", "nlopt_remove_inequality_constraints", (DL_FUNC) &nlopt_remove_inequality_constraints); R_RegisterCCallable("nloptr", "nlopt_add_inequality_constraint", (DL_FUNC) &nlopt_add_inequality_constraint); R_RegisterCCallable("nloptr", "nlopt_add_precond_inequality_constraint", (DL_FUNC) &nlopt_add_precond_inequality_constraint); R_RegisterCCallable("nloptr", "nlopt_add_inequality_mconstraint", (DL_FUNC) &nlopt_add_inequality_mconstraint); R_RegisterCCallable("nloptr", "nlopt_remove_equality_constraints", (DL_FUNC) &nlopt_remove_equality_constraints); R_RegisterCCallable("nloptr", "nlopt_add_equality_constraint", (DL_FUNC) &nlopt_add_equality_constraint); R_RegisterCCallable("nloptr", "nlopt_add_precond_equality_constraint", (DL_FUNC) &nlopt_add_precond_equality_constraint); R_RegisterCCallable("nloptr", "nlopt_add_equality_mconstraint", (DL_FUNC) &nlopt_add_equality_mconstraint); R_RegisterCCallable("nloptr", "nlopt_set_stopval", (DL_FUNC) &nlopt_set_stopval); R_RegisterCCallable("nloptr", "nlopt_get_stopval", (DL_FUNC) &nlopt_get_stopval); R_RegisterCCallable("nloptr", "nlopt_set_ftol_rel", (DL_FUNC) &nlopt_set_ftol_rel); R_RegisterCCallable("nloptr", "nlopt_get_ftol_rel", (DL_FUNC) &nlopt_get_ftol_rel); R_RegisterCCallable("nloptr", "nlopt_set_ftol_abs", (DL_FUNC) &nlopt_set_ftol_abs); R_RegisterCCallable("nloptr", "nlopt_get_ftol_abs", (DL_FUNC) &nlopt_get_ftol_abs); R_RegisterCCallable("nloptr", "nlopt_set_xtol_rel", (DL_FUNC) &nlopt_set_xtol_rel); R_RegisterCCallable("nloptr", "nlopt_get_xtol_rel", (DL_FUNC) &nlopt_get_xtol_rel); R_RegisterCCallable("nloptr", "nlopt_set_xtol_abs1", (DL_FUNC) &nlopt_set_xtol_abs1); R_RegisterCCallable("nloptr", "nlopt_set_xtol_abs", (DL_FUNC) &nlopt_set_xtol_abs); R_RegisterCCallable("nloptr", "nlopt_get_xtol_abs", (DL_FUNC) &nlopt_get_xtol_abs); R_RegisterCCallable("nloptr", "nlopt_set_maxeval", (DL_FUNC) &nlopt_set_maxeval); R_RegisterCCallable("nloptr", "nlopt_get_maxeval", (DL_FUNC) &nlopt_get_maxeval); R_RegisterCCallable("nloptr", "nlopt_set_maxtime", (DL_FUNC) &nlopt_set_maxtime); R_RegisterCCallable("nloptr", "nlopt_get_maxtime", (DL_FUNC) &nlopt_get_maxtime); R_RegisterCCallable("nloptr", "nlopt_force_stop", (DL_FUNC) &nlopt_force_stop); R_RegisterCCallable("nloptr", "nlopt_set_force_stop", (DL_FUNC) &nlopt_set_force_stop); R_RegisterCCallable("nloptr", "nlopt_get_force_stop", (DL_FUNC) &nlopt_get_force_stop); R_RegisterCCallable("nloptr", "nlopt_set_local_optimizer", (DL_FUNC) &nlopt_set_local_optimizer); R_RegisterCCallable("nloptr", "nlopt_set_population", (DL_FUNC) &nlopt_set_population); R_RegisterCCallable("nloptr", "nlopt_get_population", (DL_FUNC) &nlopt_get_population); R_RegisterCCallable("nloptr", "nlopt_set_vector_storage", (DL_FUNC) &nlopt_set_vector_storage); R_RegisterCCallable("nloptr", "nlopt_get_vector_storage", (DL_FUNC) &nlopt_get_vector_storage); R_RegisterCCallable("nloptr", "nlopt_set_default_initial_step", (DL_FUNC) &nlopt_set_default_initial_step); R_RegisterCCallable("nloptr", "nlopt_set_initial_step", (DL_FUNC) &nlopt_set_initial_step); R_RegisterCCallable("nloptr", "nlopt_set_initial_step1", (DL_FUNC) &nlopt_set_initial_step1); R_RegisterCCallable("nloptr", "nlopt_get_initial_step", (DL_FUNC) &nlopt_get_initial_step); // Register routines to improve lookup from R using .Call interface. R_registerRoutines(info, NULL, CallEntries, NULL, NULL); R_useDynamicSymbols(info, FALSE); R_forceSymbols(info, TRUE); } nloptr/src/Makevars.ucrt0000644000176200001440000000010214472612401015021 0ustar liggesusersPKG_CPPFLAGS = -I$(R_TOOLS_SOFT)/include/nlopt PKG_LIBS = -lnlopt nloptr/src/dummy.cpp0000644000176200001440000000000014472612401014205 0ustar liggesusersnloptr/src/Makevars.in0000644000176200001440000000013514763300100014451 0ustar liggesusersPKG_CPPFLAGS = @NLOPT_CPPFLAGS@ PKG_LIBS = $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS) @NLOPT_LIBS@ nloptr/src/scripts/0000755000176200001440000000000014765070675014067 5ustar liggesusersnloptr/src/scripts/nlopt_cleanup.sh0000644000176200001440000000005014763300100017232 0ustar liggesusers#!/bin/sh rm -fr nlopt-src nlopt-build nloptr/src/scripts/r_config.sh0000755000176200001440000000231514762774214016212 0ustar liggesusers#### R CONFIGURATION #### R_ARCH_BIN=$1 CC=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config CC` echo set CC=$CC export CC CPPFLAGS=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config CPPFLAGS` CFLAGS=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config CFLAGS` CPICFLAGS=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config CPICFLAGS` CFLAGS="$CPPFLAGS $CPICFLAGS $CFLAGS" echo set CFLAGS=$CFLAGS export CFLAGS CXX=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config CXX11` echo set CXX=$CXX export CXX CXXSTD=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config CXX11STD` CXXFLAGS=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config CXX11FLAGS` CXXPICFLAGS=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config CXX11PICFLAGS` CXXFLAGS="$CXXSTD $CPPFLAGS $CXXPICFLAGS $CXXFLAGS" echo set CXXFLAGS=$CXXFLAGS export CXXFLAGS LDFLAGS=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config LDFLAGS` echo set LDFLAGS=$LDFLAGS export LDFLAGS if test -z "$CXX"; then echo >&2 "Could not detect C++ compiler with R CMD config." fi ${R_HOME}/bin${R_ARCH_BIN}/Rscript --vanilla -e 'getRversion() > "4.0.0"' | grep TRUE > /dev/null if [ $? -eq 0 ]; then AR=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config AR` AR=`which $AR` RANLIB=`"${R_HOME}/bin${R_ARCH_BIN}/R" CMD config RANLIB` RANLIB=`which $RANLIB` fi nloptr/src/scripts/nlopt_download.sh0000644000176200001440000000021714765070675017446 0ustar liggesusers#! /bin/sh RSCRIPT_BIN=$1 # Uncompress NLOPT source ${RSCRIPT_BIN} -e "utils::untar(tarfile = 'nlopt-src.tar.gz')" mv nlopt-2.10.0 nlopt-src nloptr/src/nloptr.h0000644000176200001440000000026514763523341014061 0ustar liggesusers#ifndef __NLOPTR_H__ #define __NLOPTR_H__ #include #include // Rdefines.h is no longer maintained. SEXP NLoptR_Optimize(SEXP args); #endif /*__NLOPTR_H__*/ nloptr/src/nloptr.c0000644000176200001440000011153414765045541014061 0ustar liggesusers/* * Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. * This code is published under the L-GPL. * * This program is free software: you can redistribute it and/or modify * it under the terms of the GNU Lesser General Public License as published * by the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public License * along with this program. If not, see . * * File: nloptr.cpp * Author: Jelmer Ypma * Date: 9 June 2010 * * This file defines the main function NLoptR_Minimize, which * provides an interface to NLopt from R. * * The function takes an R object containing objective function, * constraints, options, etc. as argument, solve the problem * using NLopt and return the results. * * Financial support of the UK Economic and Social Research Council * through a grant (RES-589-28-0001) to the ESRC Centre for Microdata * Methods and Practice (CeMMAP) is gratefully acknowledged. * * 2011-01-13: added print_level option * 2011-07-24: added checks on return value when setting equality constraints * etc. * 2013-11-05: Moved declaration of ineq_constr_data and eq_constr_data outside * if-statement to solve segfault on Ubuntu. * 2024-07-02: Updated old include which is no longer maintained and other * minor code tweaks and efficiency enhancements (Avraham Adler). */ // TODO: add minimize/maximize option (objective = "maximize") // nlopt_result nlopt_set_min_objective(nlopt_opt opt, nlopt_func f, void* f_data); // nlopt_result nlopt_set_max_objective(nlopt_opt opt, nlopt_func f, void* f_data); #include #include "nloptr.h" #define AS_INTEGER(x) Rf_coerceVector(x, INTSXP) #define AS_REAL(x) Rf_coerceVector(x, REALSXP) // Extracts element with name 'str' from R object 'list' & returns that element. SEXP getListElement (SEXP list, char *str) { SEXP elmt = R_NilValue, names = getAttrib(list, R_NamesSymbol); for (size_t i = 0; i < length(list); i++) { if(strcmp(CHAR(STRING_ELT(names, i)), str) == 0) { elmt = VECTOR_ELT(list, i); break; } } return elmt; } // Convert the algorithm lookup from a nested if-else chain to a lookup table // and switch statement. See https://stackoverflow.com/a/49215742/2726543 typedef struct algpair { char *key; int value; } ALGPAIR; // The algtable table must be in sorted order for bsearch to work properly. ALGPAIR algtable[] = { {"NLOPT_GD_MLSL", 1}, {"NLOPT_GD_MLSL_LDS", 2}, {"NLOPT_GD_STOGO", 3}, {"NLOPT_GD_STOGO_RAND", 4}, {"NLOPT_GN_CRS2_LM", 5}, {"NLOPT_GN_DIRECT", 6}, {"NLOPT_GN_DIRECT_L", 7}, {"NLOPT_GN_DIRECT_L_NOSCAL", 8}, {"NLOPT_GN_DIRECT_L_RAND", 9}, {"NLOPT_GN_DIRECT_L_RAND_NOSCAL", 10}, {"NLOPT_GN_DIRECT_NOSCAL", 11}, {"NLOPT_GN_ESCH", 12}, {"NLOPT_GN_ISRES", 13}, {"NLOPT_GN_MLSL", 14}, {"NLOPT_GN_MLSL_LDS", 15}, {"NLOPT_GN_ORIG_DIRECT", 16}, {"NLOPT_GN_ORIG_DIRECT_L", 17}, {"NLOPT_LD_AUGLAG", 18}, {"NLOPT_LD_AUGLAG_EQ", 19}, {"NLOPT_LD_CCSAQ", 20}, {"NLOPT_LD_LBFGS", 21}, {"NLOPT_LD_LBFGS_NOCEDAL", 22}, {"NLOPT_LD_MMA", 23}, {"NLOPT_LD_SLSQP", 24}, {"NLOPT_LD_TNEWTON", 25}, {"NLOPT_LD_TNEWTON_PRECOND", 26}, {"NLOPT_LD_TNEWTON_PRECOND_RESTART", 27}, {"NLOPT_LD_TNEWTON_RESTART", 28}, {"NLOPT_LD_VAR1", 29}, {"NLOPT_LD_VAR2", 30}, {"NLOPT_LN_AUGLAG", 31}, {"NLOPT_LN_AUGLAG_EQ", 32}, {"NLOPT_LN_BOBYQA", 33}, {"NLOPT_LN_COBYLA", 34}, {"NLOPT_LN_NELDERMEAD", 35}, {"NLOPT_LN_NEWUOA", 36}, {"NLOPT_LN_NEWUOA_BOUND", 37}, {"NLOPT_LN_PRAXIS", 38}, {"NLOPT_LN_SBPLX", 39}, }; static int compAlg(const void *va, const void *vb) { const ALGPAIR *a = va, *b = vb; return strcmp(a->key, b->key); } int getVal(char *key) { ALGPAIR key_pair[1] = {{key}}; ALGPAIR *pair = bsearch(key_pair, algtable, sizeof algtable / sizeof algtable[0], sizeof algtable[0], compAlg); return pair ? pair->value : -1; } // Convert passed string to an nlopt_algorithm item. nlopt_algorithm getAlgorithmCode(const char *algorithm_str) { nlopt_algorithm algorithm; switch(getVal((char*)algorithm_str)) { case 1: algorithm = NLOPT_GD_MLSL; break; case 2: algorithm = NLOPT_GD_MLSL_LDS; break; case 3: algorithm = NLOPT_GD_STOGO; break; case 4: algorithm = NLOPT_GD_STOGO_RAND; break; case 5: algorithm = NLOPT_GN_CRS2_LM; break; case 6: algorithm = NLOPT_GN_DIRECT; break; case 7: algorithm = NLOPT_GN_DIRECT_L; break; case 8: algorithm = NLOPT_GN_DIRECT_L_NOSCAL; break; case 9: algorithm = NLOPT_GN_DIRECT_L_RAND; break; case 10: algorithm = NLOPT_GN_DIRECT_L_RAND_NOSCAL; break; case 11: algorithm = NLOPT_GN_DIRECT_NOSCAL; break; case 12: algorithm = NLOPT_GN_ESCH; break; case 13: algorithm = NLOPT_GN_ISRES; break; case 14: algorithm = NLOPT_GN_MLSL; break; case 15: algorithm = NLOPT_GN_MLSL_LDS; break; case 16: algorithm = NLOPT_GN_ORIG_DIRECT; break; case 17: algorithm = NLOPT_GN_ORIG_DIRECT_L; break; case 18: algorithm = NLOPT_LD_AUGLAG; break; case 19: algorithm = NLOPT_LD_AUGLAG_EQ; break; case 20: algorithm = NLOPT_LD_CCSAQ; break; case 21: algorithm = NLOPT_LD_LBFGS; break; case 22: #ifdef HAVE_NLOPT_LD_LBFGS_NOCEDAL algorithm = NLOPT_LD_LBFGS_NOCEDAL; #else algorithm = NLOPT_LD_LBFGS; #endif break; case 23: algorithm = NLOPT_LD_MMA; break; case 24: algorithm = NLOPT_LD_SLSQP; break; case 25: algorithm = NLOPT_LD_TNEWTON; break; case 26: algorithm = NLOPT_LD_TNEWTON_PRECOND; break; case 27: algorithm = NLOPT_LD_TNEWTON_PRECOND_RESTART; break; case 28: algorithm = NLOPT_LD_TNEWTON_RESTART; break; case 29: algorithm = NLOPT_LD_VAR1; break; case 30: algorithm = NLOPT_LD_VAR2; break; case 31: algorithm = NLOPT_LN_AUGLAG; break; case 32: algorithm = NLOPT_LN_AUGLAG_EQ; break; case 33: algorithm = NLOPT_LN_BOBYQA; break; case 34: algorithm = NLOPT_LN_COBYLA; break; case 35: algorithm = NLOPT_LN_NELDERMEAD; break; case 36: algorithm = NLOPT_LN_NEWUOA; break; case 37: algorithm = NLOPT_LN_NEWUOA_BOUND; break; case 38: algorithm = NLOPT_LN_PRAXIS; break; case 39: algorithm = NLOPT_LN_SBPLX; break; // # nocov start (Guarded against by is.nloptr lines 81–85.) default: // unknown algorithm code Rprintf("Error: unknown algorithm %s.\n", algorithm_str); // Not an algorithm, so this should result in a runtime error. algorithm = NLOPT_NUM_ALGORITHMS; // # nocov end } // Leave old code in commented for now in case of catastrophic failure. // if (strcmp(algorithm_str, "NLOPT_GN_DIRECT") == 0) { // algorithm = NLOPT_GN_DIRECT; // } else if (strcmp(algorithm_str, "NLOPT_GN_DIRECT_L") == 0) { // algorithm = NLOPT_GN_DIRECT_L; // } else if (strcmp(algorithm_str, "NLOPT_GN_DIRECT_L_RAND") == 0) { // algorithm = NLOPT_GN_DIRECT_L_RAND; // } else if (strcmp(algorithm_str, "NLOPT_GN_DIRECT_NOSCAL") == 0) { // algorithm = NLOPT_GN_DIRECT_NOSCAL; // } else if (strcmp(algorithm_str, "NLOPT_GN_DIRECT_L_NOSCAL") == 0) { // algorithm = NLOPT_GN_DIRECT_L_NOSCAL; // } else if (strcmp(algorithm_str, "NLOPT_GN_DIRECT_L_RAND_NOSCAL") == 0) { // algorithm = NLOPT_GN_DIRECT_L_RAND_NOSCAL; // } else if (strcmp(algorithm_str, "NLOPT_GN_ORIG_DIRECT") == 0) { // algorithm = NLOPT_GN_ORIG_DIRECT; // } else if (strcmp(algorithm_str, "NLOPT_GN_ORIG_DIRECT_L") == 0) { // algorithm = NLOPT_GN_ORIG_DIRECT_L; // } else if (strcmp(algorithm_str, "NLOPT_GD_STOGO") == 0) { // algorithm = NLOPT_GD_STOGO; // } else if (strcmp(algorithm_str, "NLOPT_GD_STOGO_RAND") == 0) { // algorithm = NLOPT_GD_STOGO_RAND; // } else if (strcmp(algorithm_str, "NLOPT_LD_SLSQP") == 0) { // algorithm = NLOPT_LD_SLSQP; // } else if (strcmp(algorithm_str, "NLOPT_LD_LBFGS_NOCEDAL") == 0) { // algorithm = NLOPT_LD_LBFGS_NOCEDAL; // } else if (strcmp(algorithm_str, "NLOPT_LD_LBFGS") == 0) { // algorithm = NLOPT_LD_LBFGS; // } else if (strcmp(algorithm_str, "NLOPT_LN_PRAXIS") == 0) { // algorithm = NLOPT_LN_PRAXIS; // } else if (strcmp(algorithm_str, "NLOPT_LD_VAR1") == 0) { // algorithm = NLOPT_LD_VAR1; // } else if (strcmp(algorithm_str, "NLOPT_LD_VAR2") == 0) { // algorithm = NLOPT_LD_VAR2; // } else if (strcmp(algorithm_str, "NLOPT_LD_TNEWTON") == 0) { // algorithm = NLOPT_LD_TNEWTON; // } else if (strcmp(algorithm_str, "NLOPT_LD_TNEWTON_RESTART") == 0) { // algorithm = NLOPT_LD_TNEWTON_RESTART; // } else if (strcmp(algorithm_str, "NLOPT_LD_TNEWTON_PRECOND") == 0) { // algorithm = NLOPT_LD_TNEWTON_PRECOND; // } else if (strcmp(algorithm_str, "NLOPT_LD_TNEWTON_PRECOND_RESTART") == 0) { // algorithm = NLOPT_LD_TNEWTON_PRECOND_RESTART; // } else if (strcmp(algorithm_str, "NLOPT_GN_CRS2_LM") == 0) { // algorithm = NLOPT_GN_CRS2_LM; // } else if (strcmp(algorithm_str, "NLOPT_GN_MLSL") == 0) { // algorithm = NLOPT_GN_MLSL; // } else if (strcmp(algorithm_str, "NLOPT_GD_MLSL") == 0) { // algorithm = NLOPT_GD_MLSL; // } else if (strcmp(algorithm_str, "NLOPT_GN_MLSL_LDS") == 0) { // algorithm = NLOPT_GN_MLSL_LDS; // } else if (strcmp(algorithm_str, "NLOPT_GD_MLSL_LDS") == 0) { // algorithm = NLOPT_GD_MLSL_LDS; // } else if (strcmp(algorithm_str, "NLOPT_LD_MMA") == 0) { // algorithm = NLOPT_LD_MMA; // } else if (strcmp(algorithm_str, "NLOPT_LD_CCSAQ") == 0) { // algorithm = NLOPT_LD_CCSAQ; // } else if (strcmp(algorithm_str, "NLOPT_LN_COBYLA") == 0) { // algorithm = NLOPT_LN_COBYLA; // } else if (strcmp(algorithm_str, "NLOPT_LN_NEWUOA") == 0) { // algorithm = NLOPT_LN_NEWUOA; // } else if (strcmp(algorithm_str, "NLOPT_LN_NEWUOA_BOUND") == 0) { // algorithm = NLOPT_LN_NEWUOA_BOUND; // } else if (strcmp(algorithm_str, "NLOPT_LN_NELDERMEAD") == 0) { // algorithm = NLOPT_LN_NELDERMEAD; // } else if (strcmp(algorithm_str, "NLOPT_LN_SBPLX") == 0) { // algorithm = NLOPT_LN_SBPLX; // } else if (strcmp(algorithm_str, "NLOPT_LN_AUGLAG") == 0) { // algorithm = NLOPT_LN_AUGLAG; // } else if (strcmp(algorithm_str, "NLOPT_LD_AUGLAG") == 0) { // algorithm = NLOPT_LD_AUGLAG; // } else if (strcmp(algorithm_str, "NLOPT_LN_AUGLAG_EQ") == 0) { // algorithm = NLOPT_LN_AUGLAG_EQ; // } else if (strcmp(algorithm_str, "NLOPT_LD_AUGLAG_EQ") == 0) { // algorithm = NLOPT_LD_AUGLAG_EQ; // } else if (strcmp(algorithm_str, "NLOPT_LN_BOBYQA") == 0) { // algorithm = NLOPT_LN_BOBYQA; // } else if (strcmp(algorithm_str, "NLOPT_GN_ISRES") == 0) { // algorithm = NLOPT_GN_ISRES; // } else if (strcmp(algorithm_str, "NLOPT_GN_ESCH") == 0) { // algorithm = NLOPT_GN_ESCH; // } else { // // unknown algorithm code // Rprintf("Error: unknown algorithm %s.\n", algorithm_str); // // Not an algorithm, so this should result in a runtime error. // algorithm = NLOPT_NUM_ALGORITHMS; // } return algorithm; } // Define structure that contains data to pass to the objective function typedef struct { SEXP R_eval_f; SEXP R_environment; size_t num_iterations; int print_level; } func_objective_data; // Define function that calls user-defined objective function in R double func_objective(unsigned n, const double *x, double *grad, void *data) { // Return the value, and the gradient if necessary, of the objective function. // Check for user interruption from R. R_CheckUserInterrupt(); func_objective_data *d = (func_objective_data *) data; // Increase number of function evaluations. d->num_iterations++; // Print status. if (d->print_level >= 1) { Rprintf("iteration: %zu\n", d->num_iterations); } // Print values of x. if (d->print_level >= 3) { if (n == 1) { Rprintf("\tx = %f\n", x[0]); } else { Rprintf("\tx = (%f", x[0]); for (size_t i = 1; i < n; i++) { Rprintf(", %f", x[i]); } Rprintf(")\n"); } } // Allocate memory for a vector of reals. This vector will contain the // elements of x, where x is the argument to the R function R_eval_f. SEXP rargs = allocVector(REALSXP, n); double *prargs = REAL(rargs); for (size_t i = 0; i < n; i++) { prargs[i] = x[i]; } // Evaluate R function R_eval_f with the control x as an argument. SEXP Rcall = PROTECT(lang2(d->R_eval_f, rargs)); SEXP result = PROTECT(eval(Rcall, d->R_environment)); // Recode the return value from SEXP to double. double obj_value; if (isNumeric(result)) { // Objective value is the only element of "result". obj_value = asReal(result); } else { // Objective value needs to be extracted from the list of return values. SEXP R_obj_value = PROTECT(getListElement(result, "objective")); // Recode the return value from SEXP to double. obj_value = asReal(R_obj_value); UNPROTECT(1); } // Print objective value. if (d->print_level >= 1) { Rprintf("\tf(x) = %f\n", obj_value); } // Handle gradient. if (grad) { // result needs to be a list in this case SEXP R_gradient = PROTECT(getListElement(result, "gradient")); // Recode the return value from SEXP to double. double *pRgrad = REAL(R_gradient); for (size_t i = 0; i < n; i++) { grad[i] = pRgrad[i]; } UNPROTECT(1); } UNPROTECT(2); return obj_value; } // Define structure that contains data to pass to the constraint function. typedef struct { SEXP R_eval_g; SEXP R_environment; int print_level; } func_constraints_ineq_data; /* * Define function that calls user-defined inequality constraints function in R * * m : number of constraints * constraints : value of the constraints evaluated at x * n : number of variables * x : point where we want to evaluate the constraints * grad : value of the gradient of the constraints, grad[i*n + j] = \frac{ \partial c_i }{ \partial x_j } * data : additional data that we need to evaluate the function (e.g. the R function) */ void func_constraints_ineq(unsigned m, double* constraints, unsigned n, const double* x, double* grad, void* data) { // Return the value (and the Jacobian) of the constraints. // Check for user interruption from R. R_CheckUserInterrupt(); func_constraints_ineq_data *d = (func_constraints_ineq_data *) data; // Allocate memory for a vector of reals. This vector will contain the // elements of x, where x is the argument to the R function R_eval_f. SEXP rargs_x = allocVector(REALSXP, n); double *prargsx = REAL(rargs_x); for (size_t i = 0; i < n; i++) { prargsx[i] = x[i]; } // Evaluate R function R_eval_g with the control x as an argument. SEXP Rcall = PROTECT(lang2(d->R_eval_g, rargs_x)); SEXP result = PROTECT(eval(Rcall, d->R_environment)); // Get the value of the constraint from the result. if (isNumeric(result)) { // Constraint values are the only element of result. so recode the return // value from SEXP to double*, by looping over constraints. double *presult = REAL(result); for (size_t i = 0; i < m; i++) { constraints[i] = presult[i]; } } else { // Constraint value should be extracted from the list of return values. SEXP R_constraints = PROTECT(getListElement(result, "constraints")); // Recode the return value from SEXP to double by looping over constraints. double *pRconst = REAL(R_constraints); for (size_t i = 0; i < m; i++) { constraints[i] = pRconst[i]; } UNPROTECT(1); } // Prsize_t inequality constraints. if (d->print_level >= 2) { if (m == 1) { Rprintf("\tg(x) = %f\n", constraints[0]); } else { Rprintf("\tg(x) = (%f", constraints[0]); for (size_t i = 1; i < m; i++) { Rprintf(", %f", constraints[i]); } Rprintf(")\n"); } } // Get the value of the gradient if needed. if (grad) { // Result needs to be a list in this case. SEXP R_gradient = PROTECT(getListElement(result, "jacobian")); /* * recode the return value from SEXP to double*, by looping over variables and constraints * We get a matrix from R with the Jacobian of the constraints * / dc_1/dx_1 dc_1/dx_2 ... dc_1/dx_n \ * | dc_2/dx_1 dc_2/dx_2 ... dc_2/dx_n | * | ... ... ... | * \ dc_m/dx_1 dc_m/dx_2 ... dc_m/dx_n / * Matrices are stored column-wise, so basically we get a vector * [dc_1/dx_1, dc_2/dx_1, ..., dc_m/dx_1, dc_1/dx_2, dc_2/dx_2, ..., dc_m/dx_2, ..., dc_1/dx_n, dc_2/dx_n, ..., dc_m/dx_n] * which we have to convert to a row-wise format for NLopt. */ double *pRgrad = REAL(R_gradient); for (size_t i = 0; i < m; i++) { size_t ni = i * n; for (size_t j = 0; j < n; j++) { grad[ni + j] = pRgrad[j * m + i]; } } UNPROTECT(1); } UNPROTECT(2); } // Define structure that contains data to pass to the constraint function. typedef struct { SEXP R_eval_g; SEXP R_environment; int print_level; } func_constraints_eq_data; /* * Define function that calls user-defined equality constraints function in R * * m : number of constraints * constraints : value of the constraints evaluated at x * n : number of variables * x : point where we want to evaluate the constraints * grad : value of the gradient of the constraints, grad[i*n + j] = \frac{ \partial c_i }{ \partial x_j } * data : additional data that we need to evaluate the function (e.g. the R function) */ void func_constraints_eq(unsigned m, double* constraints, unsigned n, const double* x, double* grad, void* data) { // Return the value (and the Jacobian) of the constraints. // Check for user interruption from R. R_CheckUserInterrupt(); func_constraints_eq_data *d = (func_constraints_eq_data *) data; // Allocate memory for a vector of reals. This vector will contain the // elements of x, where x is the argument to the R function R_eval_f. SEXP rargs_x = allocVector(REALSXP, n); double *prargsx = REAL(rargs_x); for (size_t i = 0; i < n; i++) { prargsx[i] = x[i]; } // Evaluate R function R_eval_g with the control x as an argument. SEXP Rcall = PROTECT(lang2(d->R_eval_g, rargs_x)); SEXP result = PROTECT(eval(Rcall, d->R_environment)); // Get the value of the constraint from the result. if (isNumeric(result)) { // Constraint values are the only element of result, so recode the return // value from SEXP to double*, by looping over constraints. double *presult = REAL(result); for (size_t i = 0; i < m; i++) { constraints[i] = presult[i]; } } else { // Constraint value should be extracted from the list of return values. SEXP R_constraints = PROTECT(getListElement(result, "constraints")); // Recode the return value from SEXP to double by looping over constraints. double *pRconst = REAL(R_constraints); for (size_t i = 0; i < m; i++) { constraints[i] = pRconst[i]; } UNPROTECT(1); } // Print equality constraints. if (d->print_level >= 2) { if (m == 1) { Rprintf("\th(x) = %f\n", constraints[0]); } else { Rprintf("\th(x) = (%f", constraints[0]); for (size_t i = 1; i < m; i++) { Rprintf(", %f", constraints[i]); } Rprintf(")\n"); } } // Get the value of the gradient if needed. if (grad) { // Result needs to be a list in this case. SEXP R_gradient = PROTECT(getListElement(result, "jacobian")); /* * recode the return value from SEXP to double*, by looping over variables and constraints * We get a matrix from R with the Jacobian of the constraints * / dc_1/dx_1 dc_1/dx_2 ... dc_1/dx_n \ * | dc_2/dx_1 dc_2/dx_2 ... dc_2/dx_n | * | ... ... ... | * \ dc_m/dx_1 dc_m/dx_2 ... dc_m/dx_n / * Matrices are stored column-wise, so basically we get a vector * [dc_1/dx_1, dc_2/dx_1, ..., dc_m/dx_1, dc_1/dx_2, dc_2/dx_2, ..., dc_m/dx_2, ..., dc_1/dx_n, dc_2/dx_n, ..., dc_m/dx_n] * which we have to convert to a row-wise format for NLopt. */ double *pRgrad = REAL(R_gradient); for (size_t i = 0; i < m; i++) { size_t ni = i * n; for (size_t j = 0; j < n; j++) { grad[ni + j] = pRgrad[j * m + i]; } } UNPROTECT(1); } UNPROTECT(2); } nlopt_opt getOptions(SEXP R_options, int num_controls, int *flag_encountered_error) { /* * double minf_max - stop if the objective function value drops below minf_max. (Set to -HUGE_VAL to ignore.) * double ftol_rel, * double ftol_abs - relative and absolute tolerances in the objective function value. (Set to zero to ignore.) * double xtol_rel, xtol_abs - relative and absolute tolerances in the optimization parameter values. xtol_abs * should either be NULL, in which case it is ignored (equivalent to zero tolerance), * or otherwise it should point to an array of length n containing absolute tolerances * in each parameter x[i]. Set any tolerance to zero for it to be ignored. * int maxeval - stop if the objective function is evaluated at least maxeval times. Set to zero to ignore. * double maxtime - stop if the elapsed wall-clock time, in seconds, exceeds maxtime. Set to zero to ignore. */ // Declare nlopt_result to capture error codes from setting options. nlopt_result res; // Get the algorithm from options. SEXP R_algorithm = PROTECT(getListElement(R_options, "algorithm")); // R_algorithm_str will contain the first (should be the only one) element of the list. SEXP R_algorithm_str = PROTECT(STRING_ELT(R_algorithm, 0)); const char* algorithm_str = CHAR(R_algorithm_str); nlopt_algorithm algorithm = getAlgorithmCode(algorithm_str); // Declare options. nlopt_opt opts; opts = nlopt_create(algorithm, num_controls); // algorithm and dimensionality // Get other options. // Stop when f(x) <= stopval for minimizing or >= stopval for maximizing. SEXP R_opts_stopval = PROTECT(getListElement(R_options, "stopval")); double stopval = asReal(R_opts_stopval); res = nlopt_set_stopval(opts, stopval); if (res == NLOPT_INVALID_ARGS) { *flag_encountered_error = 1; Rprintf("Error: nlopt_set_stopval returned NLOPT_INVALID_ARGS.\n"); } SEXP R_opts_ftol_rel = PROTECT(getListElement(R_options, "ftol_rel")); double ftol_rel = asReal(R_opts_ftol_rel); res = nlopt_set_ftol_rel(opts, ftol_rel); if (res == NLOPT_INVALID_ARGS) { *flag_encountered_error = 1; Rprintf("Error: nlopt_set_ftol_rel returned NLOPT_INVALID_ARGS.\n"); } SEXP R_opts_ftol_abs = PROTECT(getListElement(R_options, "ftol_abs")); double ftol_abs = asReal(R_opts_ftol_abs); res = nlopt_set_ftol_abs(opts, ftol_abs); if (res == NLOPT_INVALID_ARGS) { *flag_encountered_error = 1; Rprintf("Error: nlopt_set_ftol_abs returned NLOPT_INVALID_ARGS.\n"); } SEXP R_opts_xtol_rel = PROTECT(getListElement(R_options, "xtol_rel")); double xtol_rel = asReal(R_opts_xtol_rel); res = nlopt_set_xtol_rel(opts, xtol_rel); if (res == NLOPT_INVALID_ARGS) { *flag_encountered_error = 1; Rprintf("Error: nlopt_set_xtol_rel returned NLOPT_INVALID_ARGS.\n"); } SEXP R_opts_xtol_abs = PROTECT(getListElement(R_options, "xtol_abs")); double xtol_abs[num_controls]; for (size_t i = 0; i < num_controls; i++) { xtol_abs[i] = asReal(R_opts_xtol_abs); } res = nlopt_set_xtol_abs(opts, xtol_abs); if (res == NLOPT_INVALID_ARGS) { *flag_encountered_error = 1; Rprintf("Error: nlopt_set_xtol_abs returned NLOPT_INVALID_ARGS.\n"); } SEXP R_opts_maxeval = PROTECT(AS_INTEGER(getListElement(R_options, "maxeval"))); int maxeval = asInteger(R_opts_maxeval); res = nlopt_set_maxeval(opts, maxeval); if (res == NLOPT_INVALID_ARGS) { *flag_encountered_error = 1; Rprintf("Error: nlopt_set_maxeval returned NLOPT_INVALID_ARGS.\n"); } SEXP R_opts_maxtime = PROTECT(getListElement(R_options, "maxtime")); double maxtime = asReal(R_opts_maxtime); res = nlopt_set_maxtime(opts, maxtime); if (res == NLOPT_INVALID_ARGS) { *flag_encountered_error = 1; Rprintf("Error: nlopt_set_maxtime returned NLOPT_INVALID_ARGS.\n"); } SEXP R_opts_population = PROTECT(AS_INTEGER(getListElement(R_options, "population"))); unsigned int population = asInteger(R_opts_population); res = nlopt_set_population(opts, population); if (res == NLOPT_INVALID_ARGS) { *flag_encountered_error = 1; Rprintf("Error: nlopt_set_population returned NLOPT_INVALID_ARGS.\n"); } SEXP R_opts_vector_storage = PROTECT(AS_INTEGER(getListElement(R_options, "vector_storage"))); unsigned int vector_storage = asInteger(R_opts_vector_storage); res = nlopt_set_vector_storage(opts, vector_storage); if (res == NLOPT_INVALID_ARGS) { *flag_encountered_error = 1; Rprintf("Error: nlopt_set_vector_storage returned NLOPT_INVALID_ARGS.\n"); } SEXP R_opts_ranseed = PROTECT(AS_REAL(getListElement(R_options, "ranseed"))); unsigned long ranseed = REAL(R_opts_ranseed)[0]; // Set random seed if ranseed > 0. By default a random seed is generated from // system time. if (ranseed > 0) { nlopt_srand(ranseed); } UNPROTECT(12); return opts; } SEXP convertStatusToMessage(nlopt_result status) { // Convert message to an R object. SEXP R_status_message = PROTECT(allocVector(STRSXP, 1)); switch (status) { // Successful termination (positive return values): // (= +1) case NLOPT_SUCCESS: SET_STRING_ELT(R_status_message, 0, mkChar("NLOPT_SUCCESS: Generic success return value.")); break; // (= +2) case NLOPT_STOPVAL_REACHED: SET_STRING_ELT(R_status_message, 0, mkChar("NLOPT_STOPVAL_REACHED: Optimization stopped because stopval (above) was reached.")); break; // (= +3) case NLOPT_FTOL_REACHED: SET_STRING_ELT(R_status_message, 0, mkChar("NLOPT_FTOL_REACHED: Optimization stopped because ftol_rel or ftol_abs (above) was reached.")); break; // (= +4) case NLOPT_XTOL_REACHED: SET_STRING_ELT(R_status_message, 0, mkChar("NLOPT_XTOL_REACHED: Optimization stopped because xtol_rel or xtol_abs (above) was reached.")); break; // (= +5) case NLOPT_MAXEVAL_REACHED: SET_STRING_ELT(R_status_message, 0, mkChar("NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached.")); break; // (= +6) case NLOPT_MAXTIME_REACHED: SET_STRING_ELT(R_status_message, 0, mkChar("NLOPT_MAXTIME_REACHED: Optimization stopped because maxtime (above) was reached.")); break; // Error codes (negative return values): // (= -1) case NLOPT_FAILURE: SET_STRING_ELT(R_status_message, 0, mkChar("NLOPT_FAILURE: Generic failure code.")); break; // (= -2) case NLOPT_INVALID_ARGS: SET_STRING_ELT(R_status_message, 0, mkChar("NLOPT_INVALID_ARGS: Invalid arguments (e.g. lower bounds are bigger than upper bounds, an unknown algorithm was specified, etcetera).")); break; // (= -3) case NLOPT_OUT_OF_MEMORY: SET_STRING_ELT(R_status_message, 0, mkChar("NLOPT_OUT_OF_MEMORY: Ran out of memory.")); break; // (= -4) case NLOPT_ROUNDOFF_LIMITED: SET_STRING_ELT(R_status_message, 0, mkChar("NLOPT_ROUNDOFF_LIMITED: Roundoff errors led to a breakdown of the optimization algorithm. In this case, the returned minimum may still be useful. (e.g. this error occurs in NEWUOA if one tries to achieve a tolerance too close to machine precision.)")); break; // # nocov start - Cannot test as the nlopt_force_stop() function is not exposed to nloptr. case NLOPT_FORCED_STOP: SET_STRING_ELT(R_status_message, 0, mkChar("Halted because of a forced termination: the user called nlopt_force_stop(opt) on the optimization's nlopt_opt object opt from the user's objective function.")); // # nocov end default: SET_STRING_ELT(R_status_message, 0, mkChar("Return status not recognized.")); } UNPROTECT(1); return R_status_message; } // Constrained minimization: main package function. SEXP NLoptR_Optimize(SEXP args) { // Declare nlopt_result to capture error codes from setting options. nlopt_result res; int flag_encountered_error = 0; // Get initial values. SEXP R_init_values = PROTECT(getListElement(args, "x0")); // Number of control variables. unsigned num_controls = length(R_init_values); // Set initial values of the controls. double x0[num_controls]; double *pRinit = REAL(R_init_values); for (size_t i = 0; i < num_controls; i++) { x0[i] = pRinit[i]; } UNPROTECT(1); // Get options. SEXP R_options = PROTECT(getListElement(args, "options")); nlopt_opt opts = getOptions(R_options, num_controls, &flag_encountered_error); UNPROTECT(1); // Get local options. SEXP R_local_options = PROTECT(getListElement(args, "local_options")); if (R_local_options != R_NilValue) { // Parse list with options. nlopt_opt local_opts = getOptions(R_local_options, num_controls, &flag_encountered_error); // Add local optimizer options to global options. nlopt_set_local_optimizer(opts, local_opts); } UNPROTECT(1); // Get print_level from options. SEXP R_opts_print_level = PROTECT(AS_INTEGER(getListElement(R_options, "print_level"))); int print_level = asInteger(R_opts_print_level); UNPROTECT(1); // Get lower and upper bounds. SEXP R_lower_bounds = PROTECT(getListElement(args, "lower_bounds")); SEXP R_upper_bounds = PROTECT(getListElement(args, "upper_bounds")); // Set the upper and lower bounds of the controls. double lb[num_controls]; double ub[num_controls]; double *pRlb = REAL(R_lower_bounds); double *pRub = REAL(R_upper_bounds); for (size_t i = 0; i < num_controls; i++) { lb[i] = pRlb[i]; // lower bound ub[i] = pRub[i]; // upper bound } UNPROTECT(2); // Add upper and lower bounds to options. res = nlopt_set_lower_bounds(opts, lb); if (res == NLOPT_INVALID_ARGS) { flag_encountered_error = 1; Rprintf("Error: nlopt_set_lower_bounds returned NLOPT_INVALID_ARGS.\n"); } res = nlopt_set_upper_bounds(opts, ub); if (res == NLOPT_INVALID_ARGS) { flag_encountered_error = 1; Rprintf("Error: nlopt_set_upper_bounds returned NLOPT_INVALID_ARGS.\n"); } // Get number of inequality constraints. SEXP R_num_constraints_ineq = PROTECT(AS_INTEGER(getListElement(args, "num_constraints_ineq"))); unsigned num_constraints_ineq = asInteger(R_num_constraints_ineq); UNPROTECT(1); // Get number of equality constraints. SEXP R_num_constraints_eq = PROTECT(AS_INTEGER(getListElement(args, "num_constraints_eq"))); unsigned num_constraints_eq = asInteger(R_num_constraints_eq); UNPROTECT(1); // Get evaluation functions and environment. SEXP R_eval_f = PROTECT(getListElement(args, "eval_f")); // objective SEXP R_eval_g_ineq = PROTECT(getListElement(args, "eval_g_ineq")); // inequality constraints SEXP R_eval_g_eq = PROTECT(getListElement(args, "eval_g_eq")); // equality constraints SEXP R_environment = PROTECT(getListElement(args, "nloptr_environment")); // Define data to pass to objective function. func_objective_data objfunc_data; objfunc_data.R_eval_f = R_eval_f; objfunc_data.R_environment = R_environment; objfunc_data.num_iterations = 0; objfunc_data.print_level = print_level; // Add objective to options. res = nlopt_set_min_objective(opts, func_objective, &objfunc_data); if (res == NLOPT_INVALID_ARGS) { flag_encountered_error = 1; Rprintf("Error: nlopt_set_min_objective returned NLOPT_INVALID_ARGS.\n"); } // Inequality constraints // Declare data outside if-statement to prevent data corruption. func_constraints_ineq_data ineq_constr_data; if (num_constraints_ineq > 0) { // Get tolerances from R_options. double tol_constraints_ineq[num_constraints_ineq]; SEXP R_tol_constraints_ineq = PROTECT(getListElement(R_options, "tol_constraints_ineq")); double *pRtolineqc = REAL(R_tol_constraints_ineq); for (size_t i = 0; i < num_constraints_ineq; i++) { tol_constraints_ineq[i] = pRtolineqc[i]; } UNPROTECT(1); // Define data to pass to constraint function. ineq_constr_data.R_eval_g = R_eval_g_ineq; ineq_constr_data.R_environment = R_environment; ineq_constr_data.print_level = print_level; // Add vector-valued inequality constraint. res = nlopt_add_inequality_mconstraint(opts, num_constraints_ineq, func_constraints_ineq, &ineq_constr_data, tol_constraints_ineq); if (res == NLOPT_INVALID_ARGS) { flag_encountered_error = 1; Rprintf("Error: nlopt_add_inequality_mconstraint returned NLOPT_INVALID_ARGS.\n"); } } // Equality constraints // Declare data outside if-statement to prevent data corruption. func_constraints_eq_data eq_constr_data; if (num_constraints_eq > 0) { // Get tolerances from R_options. double tol_constraints_eq[num_constraints_eq]; SEXP R_tol_constraints_eq = PROTECT(getListElement(R_options, "tol_constraints_eq")); double *pRtoleqc = REAL(R_tol_constraints_eq); for (size_t i = 0; i=2.7.0`. * Use `NLOPT_LD_LBFGS` in place of `NLOPT_LD_LBFGS_NOCEDAL` when the latter is not available (in nlopt `v2.9.x`). * Add checks for `x0` and `eval_f` in `nloptr` (#191, @astamm). # nloptr 2.2.0 This release fixes a breaking bug which affects **nloptr** and its reverse dependencies and brings some minor tweaks and corrections along the way: * Minimal patch for build against nlopt `2.9.x` (#176, @jaganmn): specifically, the issuses were that (i) nlopt versions 2.9.x had one less algorithm in the enum list, namely `NLOPT_LD_LBFGS_NOCEDAL` was removed in these versions and put back in 2.10 and (ii) we were using `inst/include` in which we copied nlopt headers conditionally to build the package (e.g. listing it in `PKG_CPPFLAGS`) resulting in possible version conflicts. * Fix the 2 failed tests by adding one more termination criterion. * Update GHA workflows to latest versions. * Fix reverse `LinkingTo` dependencies by (i) unconditionally copying headers to `inst/include` and (ii) fixing `cmake` path search (#179, @astamm). * Fix for newly broken **kergp** package due to wrong usage of `if` statement inside `paste()` which works differently than when used inside `c()` (#180, @astamm). * Update artifact action to `v4` (#174, @eddelbuettel). * Correcting some of the unit tests in `test-banana` (#167, @aadler). * Correcting some of the unit tests in `test-global-wrapper` (#166, @aadler). * Update the code in `nloptr.c` for compatibility with the `R` API, efficiency, and formatting (#169, @aadler). * Bugfix: `ranseed` expects an unsigned long but was passed as an integer, thus reducing the range of random seeds. It is now passed as a double and converted to a long (#169, @aadler). # nloptr 2.1.1 This is a patch release to work around a bug in the CRAN checks. Specifically, one of the unit tests for the `isres()` algorithm was failing on some CRAN builds because convergence is stochastic with slightly different results even with the same fixed seed prior to calling the function. # nloptr 2.1.0 This release deprecates the default behavior of the inequality equations in any wrapper function which uses them. Currently, they are calibrated to be >= 0. This version allows for the equations to be consistent with the main `nloptr` function, which requires <= 0. In a future release, the default behavior will switch to assuming the calibration is <= 0, and eventually, the >= 0 behavior will be removed. It also includes a large number of safety and efficiency changes, and an expansion of the unit tests to 100% coverage for all files but one. The major changes include: * Reversed the direction of the inequality equations `hin` and `hinjac` in the wrapper functions which use them, bringing them into compliance with the main `nloptr` call. This addresses [Issue #148](https://github.com/astamm/nloptr/issues/148); * Cleaned the Hock-Schittkowski problem no. 100, Hartmann 6-dimensional, and Powell exponential examples. This addresses [Issue #152](https://github.com/astamm/nloptr/issues/152) and [Issue #156](https://github.com/astamm/nloptr/issues/156); * Updated roxygen version; * Updated maintainer email; * Deal with NA returns from `parallel::detectCores()` (contributed by @jeroen in PR #150); * Setup rhub v2 checks; * Update cmake installation instructions on Mac with brew (#146); * Allow use of equality constraints with COBYLA (#135); * Replaced the unit testing framework of `testthat` with `tinytest` (See [Issue #136](https://github.com/astamm/nloptr/issues/136)); * Brought coverage of `is.nloptr` to 100%. The only file not completely covered by unit tests is `nloptr.c`. The uncovered calls are error messages which get trapped by tests in R before the call gets to C; * Linted package for code correctness and consistency; * Updated vignette, DESCRIPTION, and NEWS; * Updated package website to use bootstrap 5; * Expanded unit tests: coverage now over 97% with no file below 90%; * Removed forcing `C++11`; * Added safety checks to C code; * Added many safety and efficiency enhancements to R code; * Most R code style made self-consistent; * Updated documentation and messages for accuracy and mathematical formatting * Updated Github actions; * Some bugfixes (e.g. in `isres` or the warning in `nl.grad`). Please see the commit logs for more detailed descriptions of the changes. # nloptr 2.0.3 * Improved compatibility on RHEL/CentOS by first searching for a `cmake3` binary on the `PATH` ([#104](https://github.com/astamm/nloptr/issues/104)). * Improved backward compatibility with older versions of `cmake` ([#119](https://github.com/astamm/nloptr/issues/119)). # nloptr 2.0.2 This is a patch version in which: * I link to the `nlopt` library via `nlopt/lib/libnlopt.a` instead of `-Lnlopt/lib -lnlopt` when building `nlopt` from included sources to avoid potential mess where `-lnlopt` could look for the `nlopt` library in other places and possibly link with an existing too old system build of `nlopt`. Additionally, we contacted [Simon Urbanek](https://github.com/s-u/) for updating the `nlopt` recipe for macOS users so that it does now match the latest `v2.7.1`, which should avoid `nlopt` to be built on the fly on CRAN machines. # nloptr 2.0.1 This is a release mainly for increasing direct compatibility with most user cases. In details, here is the list of changes that have been made: * Update `SystemRequirements` description to make it clearer which minimal versions of `cmake` (`>= 3.15.0`) and `nlopt` (`>= 2.7.0`) are required ([#100](https://github.com/astamm/nloptr/issues/100), [@HenrikBengtsson](https://github.com/HenrikBengtsson)). * End configuration sooner and louder if `cmake` is missing when needed with clearer message ([#103](https://github.com/astamm/nloptr/issues/103), [@eddelbuettel](https://github.com/eddelbuettel)). * Ensure system-wide installation of `cmake` in the list of suggestions to install it when missing. * Update GHA scripts to latest versions. * Configure git to always use LF line endings for configure.ac file. * Add CI for R-devel on Windows with Rtools42. * Fix for compatibility with versions of R anterior to `4.0` ([#111](https://github.com/astamm/nloptr/issues/111)). * Look for a `cmake3` binary in the current path before `cmake` for increasing compatibility with most RHEL/CentOS users ([#104](https://github.com/astamm/nloptr/issues/104), [@bhogan-mitre](https://github.com/bhogan-mitre), [@HenrikBengtsson](https://github.com/HenrikBengtsson)). # nloptr 2.0.0 ## Major changes * Use [CMake](https://cmake.org) to build `nlopt` from included sources on macOS and on Linux if no system build of NLopt (>= 2.7.0) is found. * Update included sources of NLopt to latest version (2.7.1). * Put back the ability on Linux platforms to re-use an existing external build of NLopt instead of building from the included sources (contributed by [Dirk Eddelbuettel](https://github.com/eddelbuettel), [#88](https://github.com/astamm/nloptr/issues/88)). * Now builds using NLopt from `rwinlib` on Windows current release (contributed by [Jeroen Ooms](https://github.com/jeroen), [#92](https://github.com/astamm/nloptr/issues/92)), or NLopt from `Rtools42` on Windows devel (contributed by [Tomas Kalibera](https://github.com/kalibera)). ## Minor changes * Added a `NEWS.md` file to track changes to the package. * Use markdown in Roxygen documentation. * Added a logo and a proper [**nloptr** website](https://astamm.github.io/nloptr/). * Added coverage. * Switch from Travis to Github Actions for CI. * Use Catch for unit testing C/C++ code. * Now tracking code coverage. * Update NLopt-related URLs following migration of [NLopt website](https://nlopt.readthedocs.io/en/latest/). * Fixed bug to avoid linking issues when using the C API via `#include ` in several source files. * Fix precision issue in test example `hs071` ([#81](https://github.com/astamm/nloptr/issues/81), [@Tom-python0121](https://github.com/Tom-python0121)). * Made NLopt algorithm `NLOPT_GN_ESCH` available from R interface (contributed by [Xiongtao Dai](https://github.com/xdaiISU)). # nloptr 1.2.2 (29 February 2020) * Replaced deprecated functions from [**testthat**](https://testthat.r-lib.org) framework in unit tests (contributed by [Avraham Adler](https://github.com/aadler)). ## 26 February 2020: * Fixed warnings (as requested by CRAN): R CMD config variables 'CPP' and 'CXXCPP' are deprecated. ## 20 October 2018: * Exposed CCSAQ algorithm in R interface (contributed by [Julien Chiquet](https://github.com/jchiquet)). # nloptr 1.2.1 (03 October 2018) * Build process was changed to solve issues on several OS (many thanks to the CRAN maintainers). # nloptr 1.2.0 (30 September 2018) ## 21 April 2018: * Changed installation procedure. NLopt source code is now part of nloptr package and not downloaded separately during configure in Unix systems in case NLopt library cannot be found. * Registered NLopt C functions to be used by external R package and included C API. * Documentation is generated using roxygen. ## 25 September 2017: * Fixed a bug in auglag. BOBYQA is now allowed as local solver (thanks to [Léo Belzile](https://github.com/lbelzile)). # nloptr 1.1.0 (22 August 2016) * Fixed a bug that sometimes caused segmentation faults due to an uninitialized vector of tolerances for the inequality and/or equality constraints (thanks to Florian Schwendinger). # nloptr 1.0.9 (22 March 2015) * When the problem fails with error status 6 (`NLOPT_MAXTIME_REACHED`) and `maxtime` was not set to a positive number in the options, then nloptr tries a couple more times to solve the problem. This is a new approach that should solve the bug that NLopt sometimes exits a problem stating the maximum available time has been reached, even when no limit on the time has been set. * Changed warning to message in order to show that for consistency with the rest of the package the inequality sign in the functions `auglag`, `cobyla`, `isres`, `mma`, and `slsqp` will be switched from >= to <= in a future nloptr version. # nloptr 1.0.8 (22 February 2015) * Changed description in DESCRIPTION such that it does not start with the package name (as requested by CRAN). # nloptr 1.0.7 (14 February 2015) * Changed title field in DESCRIPTION to title case (as requested by CRAN). * Added `donttest` around example in `mma` documentation. # nloptr 1.0.6 (8 February 2015) * Updated description to better reflect installation procedure on Linux when NLopt is pre-installed (as requested by CRAN). # nloptr 1.0.5 (28 January 2015) * Added non-exported functions CFlags and LdFlags to be used in packages that want to link to the NLopt C library. * For consistency with the rest of the package the inequality sign in the functions `auglag`, `cobyla`, `isres`, `mma`, and `slsqp` will be switched from >= to <= in the next nloptr version. The current version of nloptr shows a warning when using these functions with inequality constraints. This warning can be turned off with `options('nloptr.show.inequality.warning' = FALSE)`. # nloptr 1.0.4 (02 August 2014) * Increased version number to re-submit package to CRAN with CRLF line endings removed from `configure` and `configure.ac`. # nloptr 1.0.3 (25 July 2014) * Changed NLOPT_VERSION to 2.4.2 for Linux. * Changed `nloptr.default.options` from a `data.frame` to a function returning the `data.frame`. # nloptr 1.0.2 (25 July 2014) * Added configure script which tests for a system NLopt library via pkg-config and uses it if it is sufficiently recent (ie 2.4.*), and otherwise configure downloads, patches and builds the NLopt sources just how src/Makevars used to (thanks to [Dirk Eddelbuettel](https://github.com/eddelbuettel)). # nloptr 1.0.1 (05 May 2014) * All unit tests are now enabled and use the package testthat. Install the package with argument INSTALL_opt = "--install-tests" supplied to `install.packages` to install the tests. The tests can be run after installation with test_package('nloptr'). The testthat package needs to be installed and loaded to be able to run the tests. * Changed default value for maxtime option from 0.0 to -1.0. In some cases nloptr returned `NLOPT_MAXTIME_REACHED` without running any iterations with the default setting. This change solves this. * Replaced cat by message or warning. Messages can be suppressed by `suppressMessages`. # nloptr 1.0.0 (27 January 2014) * Merged wrappers from the **nloptwrap** package. # nloptr 0.9.6 (19 November 2013) * Added a line in `Makevars` to replace some code in NLopt to fix compilation on Solaris as requested by Brian Ripley. # nloptr 0.9.5 (12 November 2013) * Updated references from NLopt version 2.3 to NLopt version 2.4 in installation instructions in `INSTALL.windows`. * Added a line in `Makevars` that replaces some code related to type-casting in `NLopt-2.4/isres/isres.c`. * Changed encoding of `src/nloptr.c` from CP1252 to UTF-8. # nloptr 0.9.4 (09 November 2013) * Updated NLopt to version 2.4. * Changed tests to use unit testing package testthat (these are currently disabled). * Fixed a segfault that started to occur on the latest version of Ubuntu. * Slightly changed the build process (Removed `-lstdc++` from linker statement. A file `dummy.cpp` (with C++ extension) is added to the source directory to ensure linking with C++. Thanks to Brian Ripley for bringing this up.) # nloptr 0.9.3 (31 July 2013) * Split lines longer than 100 characters in `check.derivatives` examples in two lines to comply with new package rules. * Moved vignettes from `inst/doc` to `vignettes` to comply with new package rules. * Removed dependency on `apacite` in vignette as an update of `apacite` on CRAN resulted in errors. # nloptr 0.9.2 (11 July 2013) * Made changes in bibtex file of documentation. * Removed `CFLAGS`, `CXXFLAGS` from `Makevars`. # nloptr 0.9.0 * Introduced new `print_level = 3`. Shows values of controls (16 April 2012 on R-Forge). * Changed `Makevars` and `Makevars.win` to link to version 2.3 of NLopt compiled with `--with-cxx` option. This makes the StoGo algorithm available. (31 April 2013 on R-Forge). # nloptr 0.8.9 (18 November 2011) * Changed CRLF and CR line endings in `src/Makevars` to LF line endings to remove a warning from R CMD check. * Adopted some changes proposed by Brian Ripley to `src/Makevars.win` in order for nloptr to work with his new toolchain. # nloptr 0.8.8 (28 September 2011) * Updated `src/Makevars` to compile on Solaris. # nloptr 0.8.7 (24 September 2011) * Updated `src/Makevars` to compile on Solaris. # nloptr 0.8.6 (19 September 2011) * Updated `src/Makevars` to compile on Solaris. # nloptr 0.8.5 (03 September 2011) * Updated `src/Makevars` to compile a working binary for MacOS. # nloptr 0.8.4 (12 August 2011) * added new options: - data/nloptr.default.options.R: new file with a description of all options, mostly taken from the NLopt website (for internal use). - R/nloptr.print.options.R: function to show the description for a specific (set of) option(s). E.g. `nloptr.print.options(option="maxeval")`. `nloptr.print.options()` shows a description of all options if called without arguments. - added option to print a description of all options and their values (`print_options_doc` = TRUE/FALSE). - added option population to set the population of stochastic/global solvers (`population` = 1000). - added option ranseed which sets the random seed for stochastic solvers (`ranseed` = 3141). A value of 0 uses a random seed generated by system time. - option check_derivatives is no longer listed as a termination condition. - documented the option to set the tolerance of (in)equality constraints (`tol_constraints_eq`, `tol_constraints_ineq`). * `tests/banana_global.R`: new test file that uses the algorithms (CRS, ISRES, MLSL) and options `ranseed` and `population`. * `src/nloptr.c`: capture error codes from setting options. * `R/nloptr.print.R`: output gives 'optimal value of controls' when status = -4 (some error code), this is changed to 'current value of controls'. nloptr/configure.ac0000644000176200001440000000605214765050564014075 0ustar liggesusers## -*- mode: autoconf; autoconf-indentation: 4; -*- ## ## nloptr configure.ac ## ## nloptr -- R interface to NLopt ## ## Copyright (C) 2014-2022 Dirk Eddelbuettel ## ## This file is licensed under the GPL-2 or later just like most of my ## Open Source code, and is granted an exemption (should it be needed) ## for inclusion into nloptr # require at least autoconf 2.61 AC_PREREQ([2.69]) AC_INIT([nloptr],[2.0.0]) ## Set R_HOME, respecting an environment variable if set : ${R_HOME=$(R RHOME)} if test -z "${R_HOME}"; then AC_MSG_ERROR([Could not determine R_HOME.]) fi CXX=`"${R_HOME}/bin/R" CMD config CXX` if test -z "${CXX}"; then AC_MSG_ERROR([No C++ compiler available]) fi CXXFLAGS=`"${R_HOME}/bin/R" CMD config CXXFLAGS` CPPFLAGS=`"${R_HOME}/bin/R" CMD config CPPFLAGS` CXX11FLAGS=`"${R_HOME}/bin/R" CMD config CXX11FLAGS` AC_LANG(C++) AC_REQUIRE_CPP AC_PROG_CXX ## Default to build from source need_to_build="yes" ## But: Can we use pkg-config? AC_PATH_PROG(have_pkg_config, pkg-config, no) ## If yes, also check for whether pkg-config knows nlopt if test x"${have_pkg_config}" != x"no"; then AC_MSG_CHECKING([if pkg-config knows NLopt]) if pkg-config --exists nlopt; then AC_MSG_RESULT([yes]) ## Since nlopt has been found, test for minimal version requirement AC_MSG_CHECKING([for pkg-config checking NLopt version]) if pkg-config --atleast-version=2.7.0 nlopt; then AC_MSG_RESULT([>= 2.7.0]) nlopt_include=$(pkg-config --cflags nlopt) nlopt_libs=$(pkg-config --libs nlopt) ## copy headers to inst/include for reverse LinkingTo dependencies headers_location=$(pkg-config --variable=includedir nlopt) need_to_build="no" else AC_MSG_RESULT([insufficient: NLopt 2.7.0 or later is preferred.]) fi else AC_MSG_RESULT([no]) fi fi ## So do we need to build if test x"${need_to_build}" != x"no"; then AC_PATH_PROG(CMAKE_BIN, cmake, no) if test x"${CMAKE_BIN}" = x"no"; then . tools/cmake_config.sh if test -z "${CMAKE_BIN}"; then ## also error to end configure here AC_MSG_ERROR([Could not find 'cmake'.]) fi fi AC_MSG_RESULT([using cmake via $CMAKE_BIN]) ## 'uname -m' on M1 give x86_64 which is ... not helping machine=`"${R_HOME}/bin/Rscript" -e 'cat(Sys.info()[["machine"]])'` AC_MSG_RESULT([using NLopt via local cmake build on ${machine}]) tools/cmake_call.sh "$CMAKE_BIN" ## cmake_call.sh installs into nlopt/include, nlopt/lib nlopt_include="-Inlopt/include" nlopt_libs="nlopt/lib/libnlopt.a" ## copy headers to inst/include for reverse LinkingTo dependencies headers_location="src/nlopt/include" fi ## does the actual copy of the headers into inst/include AC_MSG_RESULT([Copying headers found in ${headers_location} into inst/include]) cp ${headers_location}/nlopt.* inst/include/ ## Now use all the values AC_SUBST([NLOPT_CPPFLAGS],["$nlopt_include"]) AC_SUBST([NLOPT_LIBS],["$nlopt_libs"]) AC_CONFIG_FILES([src/Makevars]) AC_OUTPUT nloptr/inst/0000755000176200001440000000000014765523731012562 5ustar liggesusersnloptr/inst/include/0000755000176200001440000000000014765523731014205 5ustar liggesusersnloptr/inst/include/nloptrAPI.h0000644000176200001440000004365114765050564016236 0ustar liggesusers/* * Copyright (C) 2017 Jelmer Ypma. All Rights Reserved. * This code is published under the L-GPL. * * This program is free software: you can redistribute it and/or modify * it under the terms of the GNU Lesser General Public License as published * by the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public License * along with this program. If not, see . * * File: nloptrAPI.h * Author: Jelmer Ypma * Date: 3 October 2017 * * This file provides an API for calling internal NLopt code from C within * R packages. The C functions that are registered in init_nloptr.c can be * accessed by external R packages. * * 03/10/2017: Initial version exposing nlopt_version. */ #ifndef __NLOPTRAPI_H__ #define __NLOPTRAPI_H__ #include #include #include #include /* * C functions can be exposed using the following template: * * RET_TYPE FUNCNAME(ARGTYPE_1 ARGNAME 1, ARGTYPE_2 ARGNAME_2) * { * static RET_TYPE(*fun)(ARGTYPE_1, ARGTYPE_2) = NULL; * if (fun == NULL) fun = (RET_TYPE(*)(ARGTYPE_1, ARGTYPE_2)) R_GetCCallable("nloptr","FUNCNAME"); * return fun(ARGNAME_1, ARGNAME_2); * } * */ inline NLOPT_EXTERN(const char *) nlopt_algorithm_name(nlopt_algorithm a) { static const char *(*fun)(nlopt_algorithm) = NULL; if (fun == NULL) fun = (const char *(*)(nlopt_algorithm)) R_GetCCallable("nloptr","nlopt_algorithm_name"); return fun(a); } inline NLOPT_EXTERN(void) nlopt_srand(unsigned long seed) { static void(*fun)(unsigned long) = NULL; if (fun == NULL) fun = (void(*)(unsigned long)) R_GetCCallable("nloptr","nlopt_srand"); return fun(seed); } inline NLOPT_EXTERN(void) nlopt_srand_time(void) { static void(*fun)(void) = NULL; if (fun == NULL) fun = (void(*)(void)) R_GetCCallable("nloptr","nlopt_srand_time"); return fun(); } inline NLOPT_EXTERN(void) nlopt_version(int *major, int *minor, int *bugfix) { static void(*fun)(int *, int *, int *) = NULL; if (fun == NULL) fun = (void(*)(int *, int *, int *)) R_GetCCallable("nloptr","nlopt_version"); return fun(major, minor, bugfix); } inline NLOPT_EXTERN(nlopt_opt) nlopt_create(nlopt_algorithm algorithm, unsigned n) { static nlopt_opt(*fun)(nlopt_algorithm, unsigned) = NULL; if (fun == NULL) fun = (nlopt_opt(*)(nlopt_algorithm, unsigned)) R_GetCCallable("nloptr","nlopt_create"); return fun(algorithm, n); } inline NLOPT_EXTERN(void) nlopt_destroy(nlopt_opt opt) { static void(*fun)(nlopt_opt) = NULL; if (fun == NULL) fun = (void(*)(nlopt_opt)) R_GetCCallable("nloptr","nlopt_destroy"); return fun(opt); } inline NLOPT_EXTERN(nlopt_opt) nlopt_copy(const nlopt_opt opt) { static nlopt_opt(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (nlopt_opt(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_copy"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_optimize(nlopt_opt opt, double *x, double *opt_f) { static nlopt_result(*fun)(nlopt_opt, double *, double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double *, double *)) R_GetCCallable("nloptr","nlopt_optimize"); return fun(opt, x, opt_f); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_min_objective(nlopt_opt opt, nlopt_func f, void *f_data) { static nlopt_result(*fun)(nlopt_opt, nlopt_func, void *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, nlopt_func, void *)) R_GetCCallable("nloptr","nlopt_set_min_objective"); return fun(opt, f, f_data); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_max_objective(nlopt_opt opt, nlopt_func f, void *f_data) { static nlopt_result(*fun)(nlopt_opt, nlopt_func, void *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, nlopt_func, void *)) R_GetCCallable("nloptr","nlopt_set_max_objective"); return fun(opt, f, f_data); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_precond_min_objective(nlopt_opt opt, nlopt_func f, nlopt_precond pre, void *f_data) { static nlopt_result(*fun)(nlopt_opt, nlopt_func, nlopt_precond, void *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, nlopt_func, nlopt_precond, void *)) R_GetCCallable("nloptr","nlopt_set_precond_min_objective"); return fun(opt, f, pre, f_data); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_precond_max_objective(nlopt_opt opt, nlopt_func f, nlopt_precond pre, void *f_data) { static nlopt_result(*fun)(nlopt_opt, nlopt_func, nlopt_precond, void *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, nlopt_func, nlopt_precond, void *)) R_GetCCallable("nloptr","nlopt_set_precond_max_objective"); return fun(opt, f, pre, f_data); } inline NLOPT_EXTERN(nlopt_algorithm) nlopt_get_algorithm(const nlopt_opt opt) { static nlopt_algorithm(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (nlopt_algorithm(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_algorithm"); return fun(opt); } inline NLOPT_EXTERN(unsigned) nlopt_get_dimension(const nlopt_opt opt) { static unsigned(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (unsigned(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_dimension"); return fun(opt); } /* constraints: */ inline NLOPT_EXTERN(nlopt_result) nlopt_set_lower_bounds(nlopt_opt opt, const double *lb) { static nlopt_result(*fun)(nlopt_opt, const double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, const double *)) R_GetCCallable("nloptr","nlopt_set_lower_bounds"); return fun(opt, lb); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_lower_bounds1(nlopt_opt opt, double lb) { static nlopt_result(*fun)(nlopt_opt, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double)) R_GetCCallable("nloptr","nlopt_set_lower_bounds1"); return fun(opt, lb); } inline NLOPT_EXTERN(nlopt_result) nlopt_get_lower_bounds(const nlopt_opt opt, double *lb) { static nlopt_result(*fun)(const nlopt_opt, double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(const nlopt_opt, double *)) R_GetCCallable("nloptr","nlopt_get_lower_bounds"); return fun(opt, lb); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_upper_bounds(nlopt_opt opt, const double *ub) { static nlopt_result(*fun)(nlopt_opt, const double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, const double *)) R_GetCCallable("nloptr","nlopt_set_upper_bounds"); return fun(opt, ub); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_upper_bounds1(nlopt_opt opt, double ub) { static nlopt_result(*fun)(nlopt_opt, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double)) R_GetCCallable("nloptr","nlopt_set_upper_bounds1"); return fun(opt, ub); } inline NLOPT_EXTERN(nlopt_result) nlopt_get_upper_bounds(const nlopt_opt opt, double *ub) { static nlopt_result(*fun)(const nlopt_opt, double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(const nlopt_opt, double *)) R_GetCCallable("nloptr","nlopt_get_upper_bounds"); return fun(opt, ub); } inline NLOPT_EXTERN(nlopt_result) nlopt_remove_inequality_constraints(nlopt_opt opt) { static nlopt_result(*fun)(nlopt_opt) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt)) R_GetCCallable("nloptr","nlopt_remove_inequality_constraints"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_add_inequality_constraint(nlopt_opt opt, nlopt_func fc, void *fc_data, double tol) { static nlopt_result(*fun)(nlopt_opt, nlopt_func, void *, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, nlopt_func, void *, double)) R_GetCCallable("nloptr","nlopt_add_inequality_constraint"); return fun(opt, fc, fc_data, tol); } inline NLOPT_EXTERN(nlopt_result) nlopt_add_precond_inequality_constraint( nlopt_opt opt, nlopt_func fc, nlopt_precond pre, void *fc_data, double tol) { static nlopt_result(*fun)(nlopt_opt, nlopt_func, nlopt_precond, void *, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, nlopt_func, nlopt_precond, void *, double)) R_GetCCallable("nloptr","nlopt_add_precond_inequality_constraint"); return fun(opt, fc, pre, fc_data, tol); } inline NLOPT_EXTERN(nlopt_result) nlopt_add_inequality_mconstraint(nlopt_opt opt, unsigned m, nlopt_mfunc fc, void *fc_data, const double *tol) { static nlopt_result(*fun)(nlopt_opt, unsigned, nlopt_mfunc, void *, const double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, unsigned, nlopt_mfunc, void *, const double *)) R_GetCCallable("nloptr","nlopt_add_inequality_mconstraint"); return fun(opt, m, fc, fc_data, tol); } inline NLOPT_EXTERN(nlopt_result) nlopt_remove_equality_constraints(nlopt_opt opt) { static nlopt_result(*fun)(nlopt_opt) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt)) R_GetCCallable("nloptr","nlopt_remove_equality_constraints"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_add_equality_constraint(nlopt_opt opt, nlopt_func h, void *h_data, double tol) { static nlopt_result(*fun)(nlopt_opt, nlopt_func, void *, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, nlopt_func, void *, double)) R_GetCCallable("nloptr","nlopt_add_equality_constraint"); return fun(opt, h, h_data, tol); } inline NLOPT_EXTERN(nlopt_result) nlopt_add_precond_equality_constraint( nlopt_opt opt, nlopt_func h, nlopt_precond pre, void *h_data, double tol) { static nlopt_result(*fun)(nlopt_opt, nlopt_func, nlopt_precond, void *, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, nlopt_func, nlopt_precond, void *, double)) R_GetCCallable("nloptr","nlopt_add_precond_equality_constraint"); return fun(opt, h, pre, h_data, tol); } inline NLOPT_EXTERN(nlopt_result) nlopt_add_equality_mconstraint(nlopt_opt opt, unsigned m, nlopt_mfunc h, void *h_data, const double *tol) { static nlopt_result(*fun)(nlopt_opt, unsigned, nlopt_mfunc, void *, const double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, unsigned, nlopt_mfunc, void *, const double *)) R_GetCCallable("nloptr","nlopt_add_equality_mconstraint"); return fun(opt, m, h, h_data, tol); } /* stopping criteria: */ inline NLOPT_EXTERN(nlopt_result) nlopt_set_stopval(nlopt_opt opt, double stopval) { static nlopt_result(*fun)(nlopt_opt, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double)) R_GetCCallable("nloptr","nlopt_set_stopval"); return fun(opt, stopval); } inline NLOPT_EXTERN(double) nlopt_get_stopval(const nlopt_opt opt) { static double(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (double(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_stopval"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_ftol_rel(nlopt_opt opt, double tol) { static nlopt_result(*fun)(nlopt_opt, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double)) R_GetCCallable("nloptr","nlopt_set_ftol_rel"); return fun(opt, tol); } inline NLOPT_EXTERN(double) nlopt_get_ftol_rel(const nlopt_opt opt) { static double(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (double(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_ftol_rel"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_ftol_abs(nlopt_opt opt, double tol) { static nlopt_result(*fun)(nlopt_opt, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double)) R_GetCCallable("nloptr","nlopt_set_ftol_abs"); return fun(opt, tol); } inline NLOPT_EXTERN(double) nlopt_get_ftol_abs(const nlopt_opt opt) { static double(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (double(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_ftol_abs"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_xtol_rel(nlopt_opt opt, double tol) { static nlopt_result(*fun)(nlopt_opt, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double)) R_GetCCallable("nloptr","nlopt_set_xtol_rel"); return fun(opt, tol); } inline NLOPT_EXTERN(double) nlopt_get_xtol_rel(const nlopt_opt opt) { static double(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (double(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_xtol_rel"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_xtol_abs1(nlopt_opt opt, double tol) { static nlopt_result(*fun)(nlopt_opt, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double)) R_GetCCallable("nloptr","nlopt_set_xtol_abs1"); return fun(opt, tol); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_xtol_abs(nlopt_opt opt, const double *tol) { static nlopt_result(*fun)(nlopt_opt, const double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, const double *)) R_GetCCallable("nloptr","nlopt_set_xtol_abs"); return fun(opt, tol); } inline NLOPT_EXTERN(nlopt_result) nlopt_get_xtol_abs(const nlopt_opt opt, double *tol) { static nlopt_result(*fun)(nlopt_opt, double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double *)) R_GetCCallable("nloptr","nlopt_get_xtol_abs"); return fun(opt, tol); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_maxeval(nlopt_opt opt, int maxeval) { static nlopt_result(*fun)(nlopt_opt, int) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, int)) R_GetCCallable("nloptr","nlopt_set_maxeval"); return fun(opt, maxeval); } inline NLOPT_EXTERN(int) nlopt_get_maxeval(const nlopt_opt opt) { static int(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (int(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_maxeval"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_maxtime(nlopt_opt opt, double maxtime) { static nlopt_result(*fun)(nlopt_opt, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double)) R_GetCCallable("nloptr","nlopt_set_maxtime"); return fun(opt, maxtime); } inline NLOPT_EXTERN(double) nlopt_get_maxtime(const nlopt_opt opt) { static double(*fun)(nlopt_opt) = NULL; if (fun == NULL) fun = (double(*)(nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_maxtime"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_force_stop(nlopt_opt opt) { static nlopt_result(*fun)(nlopt_opt) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt)) R_GetCCallable("nloptr","nlopt_force_stop"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_force_stop(nlopt_opt opt, int val) { static nlopt_result(*fun)(nlopt_opt, int) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, int)) R_GetCCallable("nloptr","nlopt_set_force_stop"); return fun(opt, val); } inline NLOPT_EXTERN(int) nlopt_get_force_stop(const nlopt_opt opt) { static int(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (int(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_force_stop"); return fun(opt); } /* more algorithm-specific parameters */ inline NLOPT_EXTERN(nlopt_result) nlopt_set_local_optimizer(nlopt_opt opt, const nlopt_opt local_opt) { static nlopt_result(*fun)(nlopt_opt, const nlopt_opt) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, const nlopt_opt)) R_GetCCallable("nloptr","nlopt_set_local_optimizer"); return fun(opt, local_opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_population(nlopt_opt opt, unsigned pop) { static nlopt_result(*fun)(nlopt_opt, unsigned) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, unsigned)) R_GetCCallable("nloptr","nlopt_set_population"); return fun(opt, pop); } inline NLOPT_EXTERN(unsigned) nlopt_get_population(const nlopt_opt opt) { static unsigned(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (unsigned(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_population"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_vector_storage(nlopt_opt opt, unsigned dim) { static nlopt_result(*fun)(nlopt_opt, unsigned) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, unsigned)) R_GetCCallable("nloptr","nlopt_set_vector_storage"); return fun(opt, dim); } inline NLOPT_EXTERN(unsigned) nlopt_get_vector_storage(const nlopt_opt opt) { static unsigned(*fun)(const nlopt_opt) = NULL; if (fun == NULL) fun = (unsigned(*)(const nlopt_opt)) R_GetCCallable("nloptr","nlopt_get_vector_storage"); return fun(opt); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_default_initial_step(nlopt_opt opt, const double *x) { static nlopt_result(*fun)(nlopt_opt, const double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, const double *)) R_GetCCallable("nloptr","nlopt_set_default_initial_step"); return fun(opt, x); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_initial_step(nlopt_opt opt, const double *dx) { static nlopt_result(*fun)(nlopt_opt, const double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, const double *)) R_GetCCallable("nloptr","nlopt_set_initial_step"); return fun(opt, dx); } inline NLOPT_EXTERN(nlopt_result) nlopt_set_initial_step1(nlopt_opt opt, double dx) { static nlopt_result(*fun)(nlopt_opt, double) = NULL; if (fun == NULL) fun = (nlopt_result(*)(nlopt_opt, double)) R_GetCCallable("nloptr","nlopt_set_initial_step1"); return fun(opt, dx); } inline NLOPT_EXTERN(nlopt_result) nlopt_get_initial_step(const nlopt_opt opt, const double *x, double *dx) { static nlopt_result(*fun)(const nlopt_opt, const double *, double *) = NULL; if (fun == NULL) fun = (nlopt_result(*)(const nlopt_opt, const double *, double *)) R_GetCCallable("nloptr","nlopt_get_initial_step"); return fun(opt, x, dx); } #endif /* __NLOPTRAPI_H__ */ nloptr/inst/CITATION0000644000176200001440000000150414613534413013706 0ustar liggesusersbibentry(bibtype = "Manual", header = paste("If you use NLopt in work that leads to a publication,", "we would appreciate it if you would kindly cite NLopt", "in your manuscript. Please cite both the NLopt library", "and the authors of the specific algorithm(s) that you", "employed in your work. Cite NLopt as:"), author = person(given = "Steven G.", family = "Johnson"), title = "The NLopt nonlinear-optimization package", year = "2008", url = "https://github.com/stevengj/nlopt", footer = paste("The authors and appropriate citations for the specific", "optimization algorithms in NLopt are listed in the", "NLopt Algorithms page.") ) nloptr/inst/doc/0000755000176200001440000000000014765523731013327 5ustar liggesusersnloptr/inst/doc/nloptr.html0000644000176200001440000016336114765523731015545 0ustar liggesusers nloptr

nloptr

Jelmer Ypma, Aymeric Stamm, and Avraham Adler

2025-03-16

This document is an introduction to nloptr: an R interface to NLopt. NLopt is a free/open-source library for nonlinear optimization, started by Steven G. Johnson, providing a common interface for a number of different free optimization routines available online as well as original implementations of various other algorithms. The NLopt library is available under the GNU Lesser General Public License (LGPL), and the copyrights are owned by a variety of authors. This package should be considered in beta and comments about any aspect of the package are welcome. This document is an R vignette prepared with the aid of knitr (Xie 2014, 2015, 2016). Financial support of the UK Economic and Social Research Council through a grant (RES-589-28-0001) to the ESRC Centre for Microdata Methods and Practice (CeMMAP) is gratefully acknowledged.

Introduction

NLopt addresses general nonlinear optimization problems of the form: \[ \begin{aligned} &\min_{x \in R^n} f(x) \\ s.t.& g(x) \leq 0 \\ & h(x) = 0 \\ & x_L \leq x \leq x_U \end{aligned} \]

where \(f(\cdot)\) is the objective function and \(x\) represents the \(n\) optimization parameters. This problem may optionally be subject to the bound constraints (also called box constraints), \(x_L\) and \(x_U\). For partially or totally unconstrained problems the bounds can take values \(-\infty\) or \(\infty\). One may also optionally have \(m\) nonlinear inequality constraints—sometimes called a nonlinear programming problem—which may be specified in \(g(\cdot)\), and equality constraints which may be specified in \(h(\cdot)\). Note that not all of the algorithms in NLopt can handle constraints.

This vignette describes how to formulate minimization problems to be solved with the R interface to NLopt. If you want to use the C interface directly or are interested in the Matlab interface, there are other sources of documentation available. Some of the information here has been taken from the NLopt website, where more details are available. All credit for implementing the C code for the different algorithms available in NLopt should go to the respective authors. Also, please see the website for information on how to cite NLopt and the algorithms you use.

Installation

This package is on CRAN and can be installed from within R using

install.packages("nloptr")

or

install.packages("nloptr", type = "source")

to install the package from source. You should now be able to load the R interface to NLopt and read the help.

library("nloptr")
?nloptr

The most recent experimental source version of nloptr can be installed from Github using the remotes package:

# install.packages("remotes")
remotes::install_github("astamm/nloptr")

Minimizing the Rosenbrock Banana function

As a first example we will solve an unconstrained minimization problem. The function we look at is the Rosenbrock Banana function: \[ f(x) = 100 \left(x_2-x_1^2\right)^2 + \left(1-x_1\right)^2, \]

which is also used as an example in the documentation for the standard R optimizer optim. The gradient of the objective function is given by: \[ \nabla f(x) = \left(\begin{array}[1]{c} -400 \cdot x_1 \cdot (x_2 - x_1^2) - 2 \cdot (1 - x_1) \\ 200 \cdot (x_2 - x_1^2) \end{array} \right). \]

Not all of the algorithms in NLopt need gradients to be supplied by the user. We will show examples with and without supplying the gradient. After loading the library.

library(nloptr)

We start by specifying the objective function and its gradient:

## Rosenbrock Banana function
eval_f <- function(x) {
  100 * (x[2] - x[1] * x[1]) ^ 2 + (1 - x[1]) ^ 2
}

## Gradient of Rosenbrock Banana function
eval_grad_f <- function(x) {
  c(-400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]),
    200 * (x[2] - x[1] * x[1]))
}

We define initial values

# initial values
x0 <- c(-1.2, 1)

and then minimize the function using the nloptr command. This command runs some checks on the supplied inputs and returns an object with the exit code of the solver, the optimal value of the objective function and the solution. Before we can minimize the function we need to specify which algorithm we want to use

opts <- list("algorithm" = "NLOPT_LD_LBFGS",
             "xtol_rel" = 1.0e-8)

Here we use the L-BFGS algorithm (Nocedal 1980; Liu and Nocedal 1989). The characters LD in the algorithm show that this algorithm looks for local minima (L) using a derivative-based (D) algorithm. Other algorithms look for global (G) minima, or they don’t need derivatives (N). We also specified the termination criterium in terms of the relative x-tolerance. Other termination criteria are available (see Appendix \ref{sec:descoptions} for a full list of options). We then solve the minimization problem using

# solve Rosenbrock Banana function
res <- nloptr(x0 = x0,
              eval_f = eval_f,
              eval_grad_f = eval_grad_f,
              opts = opts)

We can see the results by printing the resulting object.

print(res)
## 
## Call:
## 
## nloptr(x0 = x0, eval_f = eval_f, eval_grad_f = eval_grad_f, opts = opts)
## 
## 
## 
## Minimization using NLopt version 2.10.0 
## 
## NLopt solver status: 1 ( NLOPT_SUCCESS: Generic success 
## return value. )
## 
## Number of Iterations....: 56 
## Termination conditions:  xtol_rel: 1e-08 
## Number of inequality constraints:  0 
## Number of equality constraints:    0 
## Optimal value of objective function:  7.35727226897802e-23 
## Optimal value of controls: 1 1

Sometimes the objective function and its gradient contain common terms. To economize on calculations, we can return the objective and its gradient in a list. For the Rosenbrock Banana function we have for instance:

## Rosenbrock Banana function and gradient in one function
eval_f_list <- function(x) {
  common_term <- x[2] - x[1] * x[1]
  list("objective" = 100 * common_term ^ 2 + (1 - x[1]) ^ 2,
       "gradient"  = c(-400 * x[1] * common_term - 2 * (1 - x[1]),
                       200 * common_term))
}

which we minimize using

res <- nloptr(x0 = x0,
              eval_f = eval_f_list,
              opts = opts)
print(res)
## 
## Call:
## nloptr(x0 = x0, eval_f = eval_f_list, opts = opts)
## 
## 
## Minimization using NLopt version 2.10.0 
## 
## NLopt solver status: 1 ( NLOPT_SUCCESS: Generic success 
## return value. )
## 
## Number of Iterations....: 56 
## Termination conditions:  xtol_rel: 1e-08 
## Number of inequality constraints:  0 
## Number of equality constraints:    0 
## Optimal value of objective function:  7.35727226897802e-23 
## Optimal value of controls: 1 1

This gives the same results as before.

Minimization with inequality constraints

This section shows how to minimize a function subject to inequality constraints. This example is the same as the one used in the tutorial on the NLopt website. The problem we want to solve is:

\[ \begin{aligned} &\min_{x \in R^n} \sqrt{x_2} \\ s.t.& x_2 \geq 0 \\ & x_2 \geq (a_1 x_1 + b_1)^3 \\ & x_2 \geq (a_2 x_1 + b_2)^3, \end{aligned} \]

where \(a_1 = 2\), \(b_1 = 0\), \(a_2 = -1\), and \(b_2 = 1\). In order to solve this problem, we first have to re-formulate the constraints to be of the form \(g(x) \leq 0\). Note that the first constraint is a bound on \(x_2\), which we will add later. The other two constraints can be re-written as:

\[ \begin{aligned} (a_1 x_1 + b_1)^3 - x_2 &\leq 0 \\ (a_2 x_1 + b_2)^3 - x_2 &\leq 0 \end{aligned} \]

First, define R functions to calculate the objective function and its gradient:

# objective function
eval_f0 <- function(x, a, b) {
  sqrt(x[2])
}

# gradient of objective function
eval_grad_f0 <- function(x, a, b) {
  c(0, 0.5 / sqrt(x[2]))
}

If needed, these can of course be calculated in the same function as before. Then define the two constraints and the Jacobian of the constraints:

# constraint function
eval_g0 <- function(x, a, b) {
  (a * x[1] + b) ^ 3 - x[2]
}

# Jacobian of constraint
eval_jac_g0 <- function(x, a, b) {
  rbind(c(3 * a[1] * (a[1] * x[1] + b[1]) ^ 2, -1.0),
        c(3 * a[2] * (a[2] * x[1] + b[2]) ^ 2, -1.0))
}

Note that all of the functions above depend on additional parameters, a and b. We have to supply specific values for these when we invoke the optimization command. The constraint function eval_g0 returns a vector with in this case the same length as the vectors a and b. The function calculating the Jacobian of the constraint should return a matrix where the number of rows equal the number of constraints (in this case two). The number of columns should equal the number of control variables (two in this case as well).

After defining values for the parameters

# define parameters
a <- c(2, -1)
b <- c(0, 1)

we can minimize the function subject to the constraints with the following command:

# Solve using NLOPT_LD_MMA with gradient information supplied in separate
# function
res0 <- nloptr(x0 = c(1.234, 5.678),
               eval_f = eval_f0,
               eval_grad_f = eval_grad_f0,
               lb = c(-Inf, 0),
               ub = c(Inf, Inf),
               eval_g_ineq = eval_g0,
               eval_jac_g_ineq = eval_jac_g0,
               opts = list("algorithm" = "NLOPT_LD_MMA",
                           "xtol_rel" = 1.0e-8,
                           "print_level" = 2,
                           "check_derivatives" = TRUE,
                           "check_derivatives_print" = "all"),
               a = a,
               b = b)
## Checking gradients of objective function.
## Derivative checker results: 0 error(s) detected.
## 
##   eval_grad_f[1] = 0.000000e+00 ~ 0.000000e+00   [0.000000e+00]
##   eval_grad_f[2] = 2.098323e-01 ~ 2.098323e-01   [1.422937e-09]
## Checking gradients of inequality constraints.
## Derivative checker results: 0 error(s) detected.
## 
##   eval_jac_g_ineq[1, 1] =  3.654614e+01 ~  3.654614e+01   [1.667794e-08]
##   eval_jac_g_ineq[2, 1] = -1.642680e-01 ~ -1.642680e-01   [2.103453e-07]
##   eval_jac_g_ineq[1, 2] = -1.000000e+00 ~ -1.000000e+00   [0.000000e+00]
##   eval_jac_g_ineq[2, 2] = -1.000000e+00 ~ -1.000000e+00   [0.000000e+00]
## iteration: 1
##  f(x) = 2.382855
##  g(x) = (9.354647, -5.690813)
## iteration: 2
##  f(x) = 2.356135
##  g(x) = (-0.122988, -5.549587)
## iteration: 3
##  f(x) = 2.245864
##  g(x) = (-0.531886, -5.038655)
## iteration: 4
##  f(x) = 2.019102
##  g(x) = (-3.225103, -3.931195)
## iteration: 5
##  f(x) = 1.740934
##  g(x) = (-2.676263, -2.761136)
## iteration: 6
##  f(x) = 1.404206
##  g(x) = (-1.674055, -1.676216)
## iteration: 7
##  f(x) = 1.022295
##  g(x) = (-0.748790, -0.748792)
## iteration: 8
##  f(x) = 0.685203
##  g(x) = (-0.173206, -0.173207)
## iteration: 9
##  f(x) = 0.552985
##  g(x) = (-0.009496, -0.009496)
## iteration: 10
##  f(x) = 0.544354
##  g(x) = (-0.000025, -0.000025)
## iteration: 11
##  f(x) = 0.544331
##  g(x) = (0.000000, 0.000000)
## iteration: 12
##  f(x) = 0.544331
##  g(x) = (-0.000000, 0.000000)
## iteration: 13
##  f(x) = 0.544331
##  g(x) = (-0.000000, 0.000000)
## iteration: 14
##  f(x) = 0.544331
##  g(x) = (-0.000000, 0.000000)
## iteration: 15
##  f(x) = 0.544331
##  g(x) = (-0.000000, 0.000000)
## iteration: 16
##  f(x) = 0.544331
##  g(x) = (-0.000000, 0.000000)
## iteration: 17
##  f(x) = 0.544331
##  g(x) = (-0.000000, 0.000000)
## iteration: 18
##  f(x) = 0.544331
##  g(x) = (-0.000000, 0.000000)
## iteration: 19
##  f(x) = 0.544331
##  g(x) = (0.000000, 0.000000)
## iteration: 20
##  f(x) = 0.544331
##  g(x) = (-0.000000, -0.000000)
## iteration: 21
##  f(x) = 0.544331
##  g(x) = (0.000000, 0.000000)
print(res0)
## 
## Call:
## 
## nloptr(x0 = c(1.234, 5.678), eval_f = eval_f0, eval_grad_f = eval_grad_f0, 
##     lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g0, 
##     eval_jac_g_ineq = eval_jac_g0, opts = list(algorithm = "NLOPT_LD_MMA", 
##         xtol_rel = 1e-08, print_level = 2, check_derivatives = TRUE, 
##         check_derivatives_print = "all"), a = a, b = b)
## 
## 
## Minimization using NLopt version 2.10.0 
## 
## NLopt solver status: 4 ( NLOPT_XTOL_REACHED: Optimization 
## stopped because xtol_rel or xtol_abs (above) was reached. 
## )
## 
## Number of Iterations....: 21 
## Termination conditions:  xtol_rel: 1e-08 
## Number of inequality constraints:  2 
## Number of equality constraints:    0 
## Optimal value of objective function:  0.54433104762009 
## Optimal value of controls: 0.3333333 0.2962963

Here we supplied lower bounds for \(x_2\) in lb. There are no upper bounds for both control variables, so we supply Inf values. If we don’t supply lower or upper bounds, plus or minus infinity is chosen by default. The inequality constraints and its Jacobian are defined using eval_g_ineq and eval_jac_g_ineq. Not all algorithms can handle inequality constraints, so we have to specify one that does, NLOPT_LD_MMA (Svanberg 2002).

We also specify the option print_level to obtain output during the optimization process. For the available print_level values, see ?nloptr. Setting the check_derivatives option to TRUE, compares the gradients supplied by the user with a finite difference approximation in the initial point (x0). When this check is run, the option check_derivatives_print can be used to print all values of the derivative checker (all (default)), only those values that result in an error (errors) or no output (none), in which case only the number of errors is shown. The tolerance that determines if a difference between the analytic gradient and the finite difference approximation results in an error can be set using the option check_derivatives_tol (default = 1e-04). The first column shows the value of the analytic gradient, the second column shows the value of the finite difference approximation, and the third column shows the relative error. Stars are added at the front of a line if the relative error is larger than the specified tolerance.

Finally, we add all the parameters that have to be passed on to the objective and constraint functions, a and b.

We can also use a different algorithm to solve the same minimization problem. The only thing we have to change is the algorithm that we want to use, in this case NLOPT_LN_COBYLA, which is an algorithm that doesn’t need gradient information (Powell 1994, 1998).

# Solve using NLOPT_LN_COBYLA without gradient information
res1 <- nloptr(x0 = c(1.234, 5.678),
               eval_f = eval_f0,
               lb = c(-Inf, 0),
               ub = c(Inf, Inf),
               eval_g_ineq = eval_g0,
               opts = list("algorithm" = "NLOPT_LN_COBYLA",
                           "xtol_rel" = 1.0e-8),
               a = a,
               b = b)
print(res1)
## 
## Call:
## 
## nloptr(x0 = c(1.234, 5.678), eval_f = eval_f0, lb = c(-Inf, 0), 
##     ub = c(Inf, Inf), eval_g_ineq = eval_g0, opts = list(algorithm = "NLOPT_LN_COBYLA", 
##         xtol_rel = 1e-08), a = a, b = b)
## 
## 
## Minimization using NLopt version 2.10.0 
## 
## NLopt solver status: 4 ( NLOPT_XTOL_REACHED: Optimization 
## stopped because xtol_rel or xtol_abs (above) was reached. 
## )
## 
## Number of Iterations....: 50 
## Termination conditions:  xtol_rel: 1e-08 
## Number of inequality constraints:  2 
## Number of equality constraints:    0 
## Optimal value of objective function:  0.544331053951819 
## Optimal value of controls: 0.3333333 0.2962963

Derivative checker

The derivative checker can be called when supplying a minimization problem to nloptr, using the options check_derivatives, check_derivatives_tol and check_derivatives_print, but it can also be used separately. For example, define the function g, with vector outcome, and its gradient g_grad:

g <- function(x, a) {
  c(x[1] - a[1],
    x[2] - a[2],
    (x[1] - a[1]) ^ 2,
    (x[2] - a[2]) ^ 2,
    (x[1] - a[1]) ^ 3,
    (x[2] - a[2]) ^ 3)
}

g_grad <- function(x, a) {
  rbind(
    c(1, 0),
    c(0, 1),
    c(2 * (x[1] - a[1]), 0),
    c(2 * (x[1] - a[1]), 2 * (x[2] - a[2])),
    c(3 * (x[1] - a[2]) ^ 2, 0),
    c(0, 3 * (x[2] - a[2]) ^ 2)
  )
}

a is some vector containing data. The gradient contains some errors in this case. By calling the function check.derivatives we can check the user-supplied analytic gradients with a finite difference approximation at a point .x.

res <- check.derivatives(
  .x = c(1, 2),
  func = g,
  func_grad = g_grad,
  check_derivatives_print = "all",
  a = c(0.3, 0.8)
)
## Derivative checker results: 2 error(s) detected.
## 
##   grad_f[1, 1] = 1.00e+00 ~ 1.00e+00   [0.000000e+00]
##   grad_f[2, 1] = 0.00e+00 ~ 0.00e+00   [0.000000e+00]
##   grad_f[3, 1] = 1.40e+00 ~ 1.40e+00   [9.579318e-09]
## * grad_f[4, 1] = 1.40e+00 ~ 0.00e+00   [1.400000e+00]
## * grad_f[5, 1] = 1.20e-01 ~ 1.47e+00   [9.183673e-01]
##   grad_f[6, 1] = 0.00e+00 ~ 0.00e+00   [0.000000e+00]
##   grad_f[1, 2] = 0.00e+00 ~ 0.00e+00   [0.000000e+00]
##   grad_f[2, 2] = 1.00e+00 ~ 1.00e+00   [0.000000e+00]
##   grad_f[3, 2] = 0.00e+00 ~ 0.00e+00   [0.000000e+00]
##   grad_f[4, 2] = 2.40e+00 ~ 2.40e+00   [1.179675e-08]
##   grad_f[5, 2] = 0.00e+00 ~ 0.00e+00   [0.000000e+00]
##   grad_f[6, 2] = 4.32e+00 ~ 4.32e+00   [2.593906e-08]

The errors are shown on screen, where the option check_derivatives_print determines the amount of output you see. The value of the analytic gradient and the value of the finite difference approximation at the supplied point is returned in a list.

res
## $analytic
##      [,1] [,2]
## [1,] 1.00 0.00
## [2,] 0.00 1.00
## [3,] 1.40 0.00
## [4,] 1.40 2.40
## [5,] 0.12 0.00
## [6,] 0.00 4.32
## 
## $finite_difference
##      [,1] [,2]
## [1,] 1.00 0.00
## [2,] 0.00 1.00
## [3,] 1.40 0.00
## [4,] 0.00 2.40
## [5,] 1.47 0.00
## [6,] 0.00 4.32
## 
## $relative_error
##              [,1]         [,2]
## [1,] 0.000000e+00 0.000000e+00
## [2,] 0.000000e+00 0.000000e+00
## [3,] 9.579318e-09 0.000000e+00
## [4,] 1.400000e+00 1.179675e-08
## [5,] 9.183673e-01 0.000000e+00
## [6,] 0.000000e+00 2.593906e-08
## 
## $flag_derivative_warning
##       [,1]  [,2]
## [1,] FALSE FALSE
## [2,] FALSE FALSE
## [3,] FALSE FALSE
## [4,]  TRUE FALSE
## [5,]  TRUE FALSE
## [6,] FALSE FALSE

Note that not all errors will be picked up by the derivative checker. For instance, if we run the check with a = c(.5, .5), one of the errors is not flagged as an error.

Notes

The .R scripts in the tests directory contain more examples. For instance, hs071.R and systemofeq.R show how to solve problems with equality constraints. See the NLopt website for more details. Please let us know if there are any of features implemented in NLopt which should be implemented in nloptr.

Sometimes the optimization procedure terminates with a message maxtime was reached without evaluating the objective function. Submitting the same problem again usually solves this problem.

Description of options

nloptr::nloptr.print.options()
## algorithm
##  possible values: NLOPT_GN_DIRECT, NLOPT_GN_DIRECT_L,
##           NLOPT_GN_DIRECT_L_RAND, NLOPT_GN_DIRECT_NOSCAL,
##           NLOPT_GN_DIRECT_L_NOSCAL,
##           NLOPT_GN_DIRECT_L_RAND_NOSCAL,
##           NLOPT_GN_ORIG_DIRECT, NLOPT_GN_ORIG_DIRECT_L,
##           NLOPT_GD_STOGO, NLOPT_GD_STOGO_RAND,
##           NLOPT_LD_SLSQP, NLOPT_LD_LBFGS, NLOPT_LN_PRAXIS,
##           NLOPT_LD_VAR1, NLOPT_LD_VAR2, NLOPT_LD_TNEWTON,
##           NLOPT_LD_TNEWTON_RESTART,
##           NLOPT_LD_TNEWTON_PRECOND,
##           NLOPT_LD_TNEWTON_PRECOND_RESTART,
##           NLOPT_GN_CRS2_LM, NLOPT_GN_MLSL, NLOPT_GD_MLSL,
##           NLOPT_GN_MLSL_LDS, NLOPT_GD_MLSL_LDS,
##           NLOPT_LD_MMA, NLOPT_LD_CCSAQ, NLOPT_LN_COBYLA,
##           NLOPT_LN_NEWUOA, NLOPT_LN_NEWUOA_BOUND,
##           NLOPT_LN_NELDERMEAD, NLOPT_LN_SBPLX,
##           NLOPT_LN_AUGLAG, NLOPT_LD_AUGLAG,
##           NLOPT_LN_AUGLAG_EQ, NLOPT_LD_AUGLAG_EQ,
##           NLOPT_LN_BOBYQA, NLOPT_GN_ISRES
##  default value:   none
## 
##  This option is required. Check the NLopt website for a description of
##  the algorithms.
## 
## stopval
##  possible values: -Inf <= stopval <= Inf
##  default value:   -Inf
## 
##  Stop minimization when an objective value <= stopval is found.
##  Setting stopval to -Inf disables this stopping criterion (default).
## 
## ftol_rel
##  possible values: ftol_rel > 0
##  default value:   0.0
## 
##  Stop when an optimization step (or an estimate of the optimum)
##  changes the objective function value by less than ftol_rel multiplied
##  by the absolute value of the function value. If there is any chance
##  that your optimum function value is close to zero, you might want to
##  set an absolute tolerance with ftol_abs as well. Criterion is
##  disabled if ftol_rel is non-positive (default).
## 
## ftol_abs
##  possible values: ftol_abs > 0
##  default value:   0.0
## 
##  Stop when an optimization step (or an estimate of the optimum)
##  changes the function value by less than ftol_abs. Criterion is
##  disabled if ftol_abs is non-positive (default).
## 
## xtol_rel
##  possible values: xtol_rel > 0
##  default value:   1.0e-04
## 
##  Stop when an optimization step (or an estimate of the optimum)
##  changes every parameter by less than xtol_rel multiplied by the
##  absolute value of the parameter. If there is any chance that an
##  optimal parameter is close to zero, you might want to set an absolute
##  tolerance with xtol_abs as well. Criterion is disabled if xtol_rel is
##  non-positive.
## 
## xtol_abs
##  possible values: xtol_abs > 0
##  default value:   rep(0.0, length(x0))
## 
##  xtol_abs is a vector of length n (the number of elements in x) giving
##  the tolerances: stop when an optimization step (or an estimate of the
##  optimum) changes every parameter x[i] by less than xtol_abs[i].
##  Criterion is disabled if all elements of xtol_abs are non-positive
##  (default).
## 
## maxeval
##  possible values: maxeval is a positive integer
##  default value:   100
## 
##  Stop when the number of function evaluations exceeds maxeval. This is
##  not a strict maximum: the number of function evaluations may exceed
##  maxeval slightly, depending upon the algorithm. Criterion is disabled
##  if maxeval is non-positive.
## 
## maxtime
##  possible values: maxtime > 0
##  default value:   -1.0
## 
##  Stop when the optimization time (in seconds) exceeds maxtime. This is
##  not a strict maximum: the time may exceed maxtime slightly, depending
##  upon the algorithm and on how slow your function evaluation is.
##  Criterion is disabled if maxtime is non-positive (default).
## 
## tol_constraints_ineq
##  possible values: tol_constraints_ineq > 0.0
##  default value:   rep(1e-8, num_constraints_ineq)
## 
##  The parameter tol_constraints_ineq is a vector of tolerances. Each
##  tolerance corresponds to one of the inequality constraints. The
##  tolerance is used for the purpose of stopping criteria only: a point
##  x is considered feasible for judging whether to stop the optimization
##  if eval_g_ineq(x) <= tol. A tolerance of zero means that NLopt will
##  try not to consider any x to be converged unless eval_g_ineq(x) is
##  strictly non-positive; generally, at least a small positive tolerance
##  is advisable to reduce sensitivity to rounding errors. By default the
##  tolerances for all inequality constraints are set to 1e-8.
## 
## tol_constraints_eq
##  possible values: tol_constraints_eq > 0.0
##  default value:   rep(1e-8, num_constraints_eq)
## 
##  The parameter tol_constraints_eq is a vector of tolerances. Each
##  tolerance corresponds to one of the equality constraints. The
##  tolerance is used for the purpose of stopping criteria only: a point
##  x is considered feasible for judging whether to stop the optimization
##  if abs(eval_g_ineq(x)) <= tol. For equality constraints, a small
##  positive tolerance is strongly advised in order to allow NLopt to
##  converge even if the equality constraint is slightly nonzero. By
##  default the tolerances for all quality constraints are set to 1e-8.
## 
## print_level
##  possible values: 0, 1, 2, or 3
##  default value:   0
## 
##  The option print_level controls how much output is shown during the
##  optimization process. Possible values: 0 (default): no output; 1:
##  show iteration number and value of objective function; 2: 1 + show
##  value of (in)equalities; 3: 2 + show value of controls.
## 
## check_derivatives
##  possible values: TRUE or FALSE
##  default value:   FALSE
## 
##  The option check_derivatives can be activated to compare the
##  user-supplied analytic gradients with finite difference
##  approximations.
## 
## check_derivatives_tol
##  possible values: check_derivatives_tol > 0.0
##  default value:   1e-04
## 
##  The option check_derivatives_tol determines when a difference between
##  an analytic gradient and its finite difference approximation is
##  flagged as an error.
## 
## check_derivatives_print
##  possible values: 'none', 'all', 'errors',
##  default value:   all
## 
##  The option check_derivatives_print controls the output of the
##  derivative checker (if check_derivatives == TRUE). All comparisons
##  are shown ('all'), only those comparisions that resulted in an error
##  ('error'), or only the number of errors is shown ('none').
## 
## print_options_doc
##  possible values: TRUE or FALSE
##  default value:   FALSE
## 
##  If TRUE, a description of all options and their current and default
##  values is printed to the screen.
## 
## population
##  possible values: population is a positive integer
##  default value:   0
## 
##  Several of the stochastic search algorithms (e.g., CRS, MLSL, and
##  ISRES) start by generating some initial population of random points
##  x. By default, this initial population size is chosen heuristically
##  in some algorithm-specific way, but the initial population can by
##  changed by setting a positive integer value for population. A
##  population of zero implies that the heuristic default will be used.
## 
## vector_storage
##  possible values: vector_storage is a positive integer
##  default value:   20
## 
##  Number of gradients to remember from previous optimization steps.
## 
## ranseed
##  possible values: ranseed is a positive integer
##  default value:   0
## 
##  For stochastic optimization algorithms, pseudorandom numbers are
##  generated. Set the random seed using ranseed if you want to use a
##  'deterministic' sequence of pseudorandom numbers, i.e. the same
##  sequence from run to run. If ranseed is 0 (default), the seed for the
##  random numbers is generated from the system time, so that you will
##  get a different sequence of pseudorandom numbers each time you run
##  your program.

References

Johnson, Steven G. n.d. “The NLopt Nonlinear-Optimization Package.” https://nlopt.readthedocs.io/en/latest/.
Liu, D. C., and J. Nocedal. 1989. “On the Limited Memory BFGS Method for Large Scale Optimization.” Math. Programming 45: 503–28.
Nocedal, J. 1980. “Updating Quasi-Newton Matrices with Limited Storage.” Math. Comput. 35: 773–82.
Powell, M. J. D. 1994. “A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation.” In Advances in Optimization and Numerical Analysis, edited by S. Gomez and J.-P. Hennart, 51–67. Kluwer Academic, Dordrecht.
———. 1998. “Direct Search Algorithms for Optimization Calculations.” Acta Numerica 7: 287–336.
Svanberg, Krister. 2002. “A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations.” SIAM J. Optim. 12 (2): 555–73.
Xie, Yihui. 2014. “Knitr: A Comprehensive Tool for Reproducible Research in R.” In Implementing Reproducible Computational Research, edited by Victoria Stodden, Friedrich Leisch, and Roger D. Peng. Chapman; Hall/CRC. https://www.routledge.com/Implementing-Reproducible-Research/Stodden-Leisch-Peng/p/book/9781466561595.
———. 2015. Dynamic Documents with R and Knitr. 2nd ed. Boca Raton, Florida: Chapman; Hall/CRC. https://yihui.org/knitr/.
———. 2016. Knitr: A General-Purpose Package for Dynamic Report Generation in r. https://yihui.org/knitr/.
nloptr/inst/doc/nloptr.Rmd0000644000176200001440000003406314613776363015322 0ustar liggesusers--- title: "nloptr" author: "Jelmer Ypma, Aymeric Stamm, and Avraham Adler" date: "`r Sys.Date()`" output: rmarkdown::html_vignette bibliography: reflist.bib nocite: | @NLopt:website vignette: > %\VignetteIndexEntry{nloptr} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r setSweaveOptions,echo=FALSE} # have an (invisible) initialization noweb chunk # to remove the default continuation prompt ">" options(continue = " ") options(width = 60) # eliminate margin space above plots options(SweaveHooks = list(fig = function() par(mar = c(5.1, 4.1, 1.1, 2.1)))) ``` This document is an introduction to `nloptr`: an R interface to NLopt. [NLopt](https://nlopt.readthedocs.io/en/latest/) is a free/open-source library for nonlinear optimization, started by Steven G. Johnson, providing a common interface for a number of different free optimization routines available online as well as original implementations of various other algorithms. The NLopt library is available under the GNU Lesser General Public License (LGPL), and the copyrights are owned by a variety of authors. This package should be considered in beta and comments about any aspect of the package are welcome. This document is an R vignette prepared with the aid of `knitr` [@Xie:2014; @Xie:2015; @Xie:2016]. Financial support of the UK Economic and Social Research Council through a grant (RES-589-28-0001) to the ESRC Centre for Microdata Methods and Practice (CeMMAP) is gratefully acknowledged. ## Introduction NLopt addresses general nonlinear optimization problems of the form: $$ \begin{aligned} &\min_{x \in R^n} f(x) \\ s.t.& g(x) \leq 0 \\ & h(x) = 0 \\ & x_L \leq x \leq x_U \end{aligned} $$ where $f(\cdot)$ is the objective function and $x$ represents the $n$ optimization parameters. This problem may optionally be subject to the bound constraints (also called box constraints), $x_L$ and $x_U$. For partially or totally unconstrained problems the bounds can take values $-\infty$ or $\infty$. One may also optionally have $m$ nonlinear inequality constraints---sometimes called a nonlinear programming problem---which may be specified in $g(\cdot)$, and equality constraints which may be specified in $h(\cdot)$. Note that not all of the algorithms in NLopt can handle constraints. This vignette describes how to formulate minimization problems to be solved with the R interface to NLopt. If you want to use the C interface directly or are interested in the Matlab interface, there are other sources of documentation available. Some of the information here has been taken from the NLopt website, where more details are available. All credit for implementing the C code for the different algorithms available in NLopt should go to the respective authors. Also, please see the [website](https://nlopt.readthedocs.io/en/latest/Citing_NLopt/) for information on how to cite NLopt and the algorithms you use. ## Installation This package is on CRAN and can be installed from within R using ```{r installNLopt, eval=FALSE} install.packages("nloptr") ``` or ```{r installNLoptSource, eval=FALSE} install.packages("nloptr", type = "source") ``` to install the package from source. You should now be able to load the R interface to NLopt and read the help. ```{r testNLoptInstallation, eval=FALSE} library("nloptr") ?nloptr ``` The most recent experimental *source* version of `nloptr` can be installed from Github using the `remotes` package: ```{r installNLoptGithub, eval=FALSE} # install.packages("remotes") remotes::install_github("astamm/nloptr") ``` ## Minimizing the Rosenbrock Banana function As a first example we will solve an unconstrained minimization problem. The function we look at is the Rosenbrock Banana function: $$ f(x) = 100 \left(x_2-x_1^2\right)^2 + \left(1-x_1\right)^2, $$ which is also used as an example in the documentation for the standard R optimizer `optim`. The gradient of the objective function is given by: $$ \nabla f(x) = \left(\begin{array}[1]{c} -400 \cdot x_1 \cdot (x_2 - x_1^2) - 2 \cdot (1 - x_1) \\ 200 \cdot (x_2 - x_1^2) \end{array} \right). $$ Not all of the algorithms in NLopt need gradients to be supplied by the user. We will show examples with and without supplying the gradient. After loading the library. ```{r loadLibrary} library(nloptr) ``` We start by specifying the objective function and its gradient: ```{r defineRosenbrockBanana} ## Rosenbrock Banana function eval_f <- function(x) { 100 * (x[2] - x[1] * x[1]) ^ 2 + (1 - x[1]) ^ 2 } ## Gradient of Rosenbrock Banana function eval_grad_f <- function(x) { c(-400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), 200 * (x[2] - x[1] * x[1])) } ``` We define initial values ```{r setRosenbrockBananaInitialValues} # initial values x0 <- c(-1.2, 1) ``` and then minimize the function using the `nloptr` command. This command runs some checks on the supplied inputs and returns an object with the exit code of the solver, the optimal value of the objective function and the solution. Before we can minimize the function we need to specify which algorithm we want to use ```{r setRosenbrockBananaOptions} opts <- list("algorithm" = "NLOPT_LD_LBFGS", "xtol_rel" = 1.0e-8) ``` Here we use the L-BFGS algorithm [@Nocedal:1980; @LiuNocedal:1989]. The characters `LD` in the algorithm show that this algorithm looks for local minima (`L`) using a derivative-based (`D`) algorithm. Other algorithms look for global (`G`) minima, or they don't need derivatives (`N`). We also specified the termination criterium in terms of the relative x-tolerance. Other termination criteria are available (see Appendix `\ref{sec:descoptions}` for a full list of options). We then solve the minimization problem using ```{r solveRosenbrockBanana} # solve Rosenbrock Banana function res <- nloptr(x0 = x0, eval_f = eval_f, eval_grad_f = eval_grad_f, opts = opts) ``` We can see the results by printing the resulting object. ```{r printRosenbrockBanana} print(res) ``` Sometimes the objective function and its gradient contain common terms. To economize on calculations, we can return the objective and its gradient in a list. For the Rosenbrock Banana function we have for instance: ```{r defineRosenbrockBananaList} ## Rosenbrock Banana function and gradient in one function eval_f_list <- function(x) { common_term <- x[2] - x[1] * x[1] list("objective" = 100 * common_term ^ 2 + (1 - x[1]) ^ 2, "gradient" = c(-400 * x[1] * common_term - 2 * (1 - x[1]), 200 * common_term)) } ``` which we minimize using ```{r solveRosenbrockBananaList} res <- nloptr(x0 = x0, eval_f = eval_f_list, opts = opts) print(res) ``` This gives the same results as before. ## Minimization with inequality constraints This section shows how to minimize a function subject to inequality constraints. This example is the same as the one used in the tutorial on the NLopt website. The problem we want to solve is: $$ \begin{aligned} &\min_{x \in R^n} \sqrt{x_2} \\ s.t.& x_2 \geq 0 \\ & x_2 \geq (a_1 x_1 + b_1)^3 \\ & x_2 \geq (a_2 x_1 + b_2)^3, \end{aligned} $$ where $a_1 = 2$, $b_1 = 0$, $a_2 = -1$, and $b_2 = 1$. In order to solve this problem, we first have to re-formulate the constraints to be of the form $g(x) \leq 0$. Note that the first constraint is a bound on $x_2$, which we will add later. The other two constraints can be re-written as: $$ \begin{aligned} (a_1 x_1 + b_1)^3 - x_2 &\leq 0 \\ (a_2 x_1 + b_2)^3 - x_2 &\leq 0 \end{aligned} $$ First, define R functions to calculate the objective function and its gradient: ```{r defineTutorialObjective} # objective function eval_f0 <- function(x, a, b) { sqrt(x[2]) } # gradient of objective function eval_grad_f0 <- function(x, a, b) { c(0, 0.5 / sqrt(x[2])) } ``` If needed, these can of course be calculated in the same function as before. Then define the two constraints and the Jacobian of the constraints: ```{r defineTutorialConstraints} # constraint function eval_g0 <- function(x, a, b) { (a * x[1] + b) ^ 3 - x[2] } # Jacobian of constraint eval_jac_g0 <- function(x, a, b) { rbind(c(3 * a[1] * (a[1] * x[1] + b[1]) ^ 2, -1.0), c(3 * a[2] * (a[2] * x[1] + b[2]) ^ 2, -1.0)) } ``` Note that all of the functions above depend on additional parameters, `a` and `b`. We have to supply specific values for these when we invoke the optimization command. The constraint function `eval_g0` returns a vector with in this case the same length as the vectors `a` and `b`. The function calculating the Jacobian of the constraint should return a matrix where the number of rows equal the number of constraints (in this case two). The number of columns should equal the number of control variables (two in this case as well). After defining values for the parameters ```{r defineTutorialParameters} # define parameters a <- c(2, -1) b <- c(0, 1) ``` we can minimize the function subject to the constraints with the following command: ```{r solveTutorialWithGradient} # Solve using NLOPT_LD_MMA with gradient information supplied in separate # function res0 <- nloptr(x0 = c(1.234, 5.678), eval_f = eval_f0, eval_grad_f = eval_grad_f0, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g0, eval_jac_g_ineq = eval_jac_g0, opts = list("algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1.0e-8, "print_level" = 2, "check_derivatives" = TRUE, "check_derivatives_print" = "all"), a = a, b = b) print(res0) ``` Here we supplied lower bounds for $x_2$ in `lb`. There are no upper bounds for both control variables, so we supply `Inf` values. If we don't supply lower or upper bounds, plus or minus infinity is chosen by default. The inequality constraints and its Jacobian are defined using `eval_g_ineq` and `eval_jac_g_ineq`. Not all algorithms can handle inequality constraints, so we have to specify one that does, `NLOPT_LD_MMA` [@Svanberg:2002]. We also specify the option `print_level` to obtain output during the optimization process. For the available `print_level` values, see `?nloptr`. Setting the `check_derivatives` option to `TRUE`, compares the gradients supplied by the user with a finite difference approximation in the initial point (`x0`). When this check is run, the option `check_derivatives_print` can be used to print all values of the derivative checker (`all` (default)), only those values that result in an error (`errors`) or no output (`none`), in which case only the number of errors is shown. The tolerance that determines if a difference between the analytic gradient and the finite difference approximation results in an error can be set using the option `check_derivatives_tol` (default = 1e-04). The first column shows the value of the analytic gradient, the second column shows the value of the finite difference approximation, and the third column shows the relative error. Stars are added at the front of a line if the relative error is larger than the specified tolerance. Finally, we add all the parameters that have to be passed on to the objective and constraint functions, `a` and `b`. We can also use a different algorithm to solve the same minimization problem. The only thing we have to change is the algorithm that we want to use, in this case `NLOPT_LN_COBYLA`, which is an algorithm that doesn't need gradient information [@Powell:1994; @Powell:1998]. ```{r solveTutorialWithoutGradient} # Solve using NLOPT_LN_COBYLA without gradient information res1 <- nloptr(x0 = c(1.234, 5.678), eval_f = eval_f0, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g0, opts = list("algorithm" = "NLOPT_LN_COBYLA", "xtol_rel" = 1.0e-8), a = a, b = b) print(res1) ``` ## Derivative checker The derivative checker can be called when supplying a minimization problem to `nloptr`, using the options `check_derivatives`, `check_derivatives_tol` and `check_derivatives_print`, but it can also be used separately. For example, define the function `g`, with vector outcome, and its gradient `g_grad`: ```{r derivativeCheckerDefineFunctions} g <- function(x, a) { c(x[1] - a[1], x[2] - a[2], (x[1] - a[1]) ^ 2, (x[2] - a[2]) ^ 2, (x[1] - a[1]) ^ 3, (x[2] - a[2]) ^ 3) } g_grad <- function(x, a) { rbind( c(1, 0), c(0, 1), c(2 * (x[1] - a[1]), 0), c(2 * (x[1] - a[1]), 2 * (x[2] - a[2])), c(3 * (x[1] - a[2]) ^ 2, 0), c(0, 3 * (x[2] - a[2]) ^ 2) ) } ``` `a` is some vector containing data. The gradient contains some errors in this case. By calling the function `check.derivatives` we can check the user-supplied analytic gradients with a finite difference approximation at a point `.x`. ```{r derivativeCheckerPrint} res <- check.derivatives( .x = c(1, 2), func = g, func_grad = g_grad, check_derivatives_print = "all", a = c(0.3, 0.8) ) ``` The errors are shown on screen, where the option `check_derivatives_print` determines the amount of output you see. The value of the analytic gradient and the value of the finite difference approximation at the supplied point is returned in a list. ```{r derivativeCheckerResult} res ``` Note that not all errors will be picked up by the derivative checker. For instance, if we run the check with `a = c(.5, .5)`, one of the errors is not flagged as an error. ## Notes The `.R` scripts in the `tests` directory contain more examples. For instance, `hs071.R` and `systemofeq.R` show how to solve problems with equality constraints. See the [NLopt website](https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#augmented-lagrangian-algorithm) for more details. Please let us know if there are any of features implemented in NLopt which should be implemented in `nloptr`. Sometimes the optimization procedure terminates with a message `maxtime was reached` without evaluating the objective function. Submitting the same problem again usually solves this problem. ## Description of options ```{r printAllOptions} nloptr::nloptr.print.options() ``` ## References nloptr/inst/doc/nloptr.R0000644000176200001440000001132414765523730014770 0ustar liggesusers## ----setSweaveOptions,echo=FALSE-------------------------- # have an (invisible) initialization noweb chunk # to remove the default continuation prompt ">" options(continue = " ") options(width = 60) # eliminate margin space above plots options(SweaveHooks = list(fig = function() par(mar = c(5.1, 4.1, 1.1, 2.1)))) ## ----installNLopt, eval=FALSE----------------------------- # install.packages("nloptr") ## ----installNLoptSource, eval=FALSE----------------------- # install.packages("nloptr", type = "source") ## ----testNLoptInstallation, eval=FALSE-------------------- # library("nloptr") # ?nloptr ## ----installNLoptGithub, eval=FALSE----------------------- # # install.packages("remotes") # remotes::install_github("astamm/nloptr") ## ----loadLibrary------------------------------------------ library(nloptr) ## ----defineRosenbrockBanana------------------------------- ## Rosenbrock Banana function eval_f <- function(x) { 100 * (x[2] - x[1] * x[1]) ^ 2 + (1 - x[1]) ^ 2 } ## Gradient of Rosenbrock Banana function eval_grad_f <- function(x) { c(-400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), 200 * (x[2] - x[1] * x[1])) } ## ----setRosenbrockBananaInitialValues--------------------- # initial values x0 <- c(-1.2, 1) ## ----setRosenbrockBananaOptions--------------------------- opts <- list("algorithm" = "NLOPT_LD_LBFGS", "xtol_rel" = 1.0e-8) ## ----solveRosenbrockBanana-------------------------------- # solve Rosenbrock Banana function res <- nloptr(x0 = x0, eval_f = eval_f, eval_grad_f = eval_grad_f, opts = opts) ## ----printRosenbrockBanana-------------------------------- print(res) ## ----defineRosenbrockBananaList--------------------------- ## Rosenbrock Banana function and gradient in one function eval_f_list <- function(x) { common_term <- x[2] - x[1] * x[1] list("objective" = 100 * common_term ^ 2 + (1 - x[1]) ^ 2, "gradient" = c(-400 * x[1] * common_term - 2 * (1 - x[1]), 200 * common_term)) } ## ----solveRosenbrockBananaList---------------------------- res <- nloptr(x0 = x0, eval_f = eval_f_list, opts = opts) print(res) ## ----defineTutorialObjective------------------------------ # objective function eval_f0 <- function(x, a, b) { sqrt(x[2]) } # gradient of objective function eval_grad_f0 <- function(x, a, b) { c(0, 0.5 / sqrt(x[2])) } ## ----defineTutorialConstraints---------------------------- # constraint function eval_g0 <- function(x, a, b) { (a * x[1] + b) ^ 3 - x[2] } # Jacobian of constraint eval_jac_g0 <- function(x, a, b) { rbind(c(3 * a[1] * (a[1] * x[1] + b[1]) ^ 2, -1.0), c(3 * a[2] * (a[2] * x[1] + b[2]) ^ 2, -1.0)) } ## ----defineTutorialParameters----------------------------- # define parameters a <- c(2, -1) b <- c(0, 1) ## ----solveTutorialWithGradient---------------------------- # Solve using NLOPT_LD_MMA with gradient information supplied in separate # function res0 <- nloptr(x0 = c(1.234, 5.678), eval_f = eval_f0, eval_grad_f = eval_grad_f0, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g0, eval_jac_g_ineq = eval_jac_g0, opts = list("algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1.0e-8, "print_level" = 2, "check_derivatives" = TRUE, "check_derivatives_print" = "all"), a = a, b = b) print(res0) ## ----solveTutorialWithoutGradient------------------------- # Solve using NLOPT_LN_COBYLA without gradient information res1 <- nloptr(x0 = c(1.234, 5.678), eval_f = eval_f0, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g0, opts = list("algorithm" = "NLOPT_LN_COBYLA", "xtol_rel" = 1.0e-8), a = a, b = b) print(res1) ## ----derivativeCheckerDefineFunctions--------------------- g <- function(x, a) { c(x[1] - a[1], x[2] - a[2], (x[1] - a[1]) ^ 2, (x[2] - a[2]) ^ 2, (x[1] - a[1]) ^ 3, (x[2] - a[2]) ^ 3) } g_grad <- function(x, a) { rbind( c(1, 0), c(0, 1), c(2 * (x[1] - a[1]), 0), c(2 * (x[1] - a[1]), 2 * (x[2] - a[2])), c(3 * (x[1] - a[2]) ^ 2, 0), c(0, 3 * (x[2] - a[2]) ^ 2) ) } ## ----derivativeCheckerPrint------------------------------- res <- check.derivatives( .x = c(1, 2), func = g, func_grad = g_grad, check_derivatives_print = "all", a = c(0.3, 0.8) ) ## ----derivativeCheckerResult------------------------------ res ## ----printAllOptions-------------------------------------- nloptr::nloptr.print.options() nloptr/inst/tinytest/0000755000176200001440000000000014765064402014440 5ustar liggesusersnloptr/inst/tinytest/test-wrapper-auglag.R0000644000176200001440000002013414633255630020455 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-auglag # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls to auglag algorithm # # Changelog: # 2023-08-23: Change _output to _stdout # library(nloptr) depMess <- paste("The old behavior for hin >= 0 has been deprecated. Please", "restate the inequality to be <=0. The ability to use the old", "behavior will be removed in a future release.") # Taken from example x0 <- c(1, 1) fn <- function(x) (x[1L] - 2) ^ 2 + (x[2L] - 1) ^ 2 hin <- function(x) 0.25 * x[1L] ^ 2 + x[2L] ^ 2 - 1 # hin <= 0 heq <- function(x) x[1L] - 2 * x[2L] + 1 # heq = 0 gr <- function(x) nl.grad(x, fn) hinjac <- function(x) nl.jacobian(x, hin) heqjac <- function(x) nl.jacobian(x, heq) hin2 <- function(x) -hin(x) # Needed to test old behavior hinjac2 <- function(x) nl.jacobian(x, hin2) # Needed to test old behavior # Test silence on proper behavior expect_silent(auglag(x0, fn)) expect_silent(auglag(x0, fn, hin = hin, deprecatedBehavior = FALSE)) # Test errors expect_error(auglag(x0, fn, ineq2local = TRUE), "Inequalities to local solver: feature not yet implemented.") expect_error(auglag(x0, fn, localsolver = "NLOPT_LN_NELDERMEAD"), "Only local solvers allowed: BOBYQA, COBYLA, LBFGS, MMA, SLSQP.") # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(auglag(x0, fn, nl.info = TRUE), "Call:", fixed = TRUE) # Test COBYLA version augTest <- auglag(x0, fn, hin = hin, heq = heq, deprecatedBehavior = FALSE) augControl <- nloptr(x0 = x0, eval_f = fn, eval_g_ineq = hin, eval_g_eq = heq, opts = list(algorithm = "NLOPT_LN_AUGLAG", xtol_rel = 1e-6, maxeval = 1000L, local_opts = list( algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-6 ))) expect_identical(augTest$par, augControl$solution) expect_identical(augTest$value, augControl$objective) expect_identical(augTest$global_solver, augControl$options$algorithm) expect_identical(augTest$local_solver, augControl$local_options$algorithm) expect_identical(augTest$convergence, augControl$status) expect_identical(augTest$message, augControl$message) # Test BOBYQA version augTest <- auglag(x0, fn, hin = hin, heq = heq, localsolver = "BOBYQA", deprecatedBehavior = FALSE) augControl <- nloptr(x0 = x0, eval_f = fn, eval_g_ineq = hin, eval_g_eq = heq, opts = list(algorithm = "NLOPT_LN_AUGLAG", xtol_rel = 1e-6, maxeval = 1000L, local_opts = list( algorithm = "NLOPT_LN_BOBYQA", xtol_rel = 1e-6 ))) expect_identical(augTest$par, augControl$solution) expect_identical(augTest$value, augControl$objective) expect_identical(augTest$global_solver, augControl$options$algorithm) expect_identical(augTest$local_solver, augControl$local_options$algorithm) expect_identical(augTest$convergence, augControl$status) expect_identical(augTest$message, augControl$message) # Test SLSQP version # No passed hin/heq Jacobian augTest <- auglag(x0, fn, hin = hin, heq = heq, localsolver = "SLSQP", deprecatedBehavior = FALSE) augControl <- nloptr(x0 = x0, eval_f = fn, eval_grad_f = gr, eval_g_ineq = hin, eval_jac_g_ineq = hinjac, eval_g_eq = heq, eval_jac_g_eq = heqjac, opts = list(algorithm = "NLOPT_LD_AUGLAG", xtol_rel = 1e-6, maxeval = 1000L, local_opts = list(algorithm = "NLOPT_LD_SLSQP", eval_grad_f = gr, xtol_rel = 1e-6))) expect_identical(augTest$par, augControl$solution) expect_identical(augTest$value, augControl$objective) expect_identical(augTest$global_solver, augControl$options$algorithm) expect_identical(augTest$local_solver, augControl$local_options$algorithm) expect_identical(augTest$convergence, augControl$status) expect_identical(augTest$message, augControl$message) # Passed hin/heq Jacobian augTest <- auglag(x0, fn, hin = hin, heq = heq, hinjac = hinjac, heqjac = heqjac, localsolver = "SLSQP", deprecatedBehavior = FALSE) expect_identical(augTest$par, augControl$solution) expect_identical(augTest$value, augControl$objective) expect_identical(augTest$global_solver, augControl$options$algorithm) expect_identical(augTest$local_solver, augControl$local_options$algorithm) expect_identical(augTest$convergence, augControl$status) expect_identical(augTest$message, augControl$message) # Test LBFGS version augTest <- auglag(x0, fn, hin = hin, heq = heq, localsolver = "LBFGS", deprecatedBehavior = FALSE) augControl <- nloptr(x0 = x0, eval_f = fn, eval_grad_f = gr, eval_g_ineq = hin, eval_jac_g_ineq = hinjac, eval_g_eq = heq, eval_jac_g_eq = heqjac, opts = list(algorithm = "NLOPT_LD_AUGLAG", xtol_rel = 1e-6, maxeval = 1000L, local_opts = list(algorithm = "NLOPT_LD_LBFGS", eval_grad_f = gr, xtol_rel = 1e-6))) expect_identical(augTest$par, augControl$solution) expect_identical(augTest$value, augControl$objective) expect_identical(augTest$global_solver, augControl$options$algorithm) expect_identical(augTest$local_solver, augControl$local_options$algorithm) expect_identical(augTest$convergence, augControl$status) expect_identical(augTest$message, augControl$message) # Test MMA version augTest <- auglag(x0, fn, hin = hin, heq = heq, localsolver = "MMA", deprecatedBehavior = FALSE) augControl <- nloptr(x0 = x0, eval_f = fn, eval_grad_f = gr, eval_g_ineq = hin, eval_jac_g_ineq = hinjac, eval_g_eq = heq, eval_jac_g_eq = heqjac, opts = list(algorithm = "NLOPT_LD_AUGLAG", xtol_rel = 1e-6, maxeval = 1000L, local_opts = list(algorithm = "NLOPT_LD_MMA", eval_grad_f = gr, xtol_rel = 1e-6))) expect_identical(augTest$par, augControl$solution) expect_identical(augTest$value, augControl$objective) expect_identical(augTest$global_solver, augControl$options$algorithm) expect_identical(augTest$local_solver, augControl$local_options$algorithm) expect_identical(augTest$convergence, augControl$status) expect_identical(augTest$message, augControl$message) # Test deprecated message expect_warning(auglag(x0, fn, hin = hin2), depMess) # Test old behavior still works augTest <- suppressWarnings(auglag(x0, fn, hin = hin2, hinjac = hinjac2, heq = heq, localsolver = "MMA")) expect_identical(augTest$par, augControl$solution) expect_identical(augTest$value, augControl$objective) expect_identical(augTest$global_solver, augControl$options$algorithm) expect_identical(augTest$local_solver, augControl$local_options$algorithm) expect_identical(augTest$convergence, augControl$status) expect_identical(augTest$message, augControl$message) nloptr/inst/tinytest/test-nloptions.R0000644000176200001440000000235014472716401017563 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-nloptions # Author: Avraham Adler # Date: 6 February 2023 # # Test code in "nloptions" function that is not tested elsewhere. # # Changelog: # library(nloptr) opts <- list( stopval = -Inf, # stop minimization at this value xtol_rel = 1e-6, # stop on small optimization step maxeval = 1000, # stop on this many function evaluations ftol_rel = 0.0, # stop on change times function value ftol_abs = 0.0, # stop on small change of function value check_derivatives = FALSE, algorithm = NULL # will be filled by each single function ) opts2 <- opts names(opts2) <- "" expect_identical(nl.opts(NULL), opts) expect_error(nl.opts("C"), "Argument `optlist` must be a named list.", fixed = TRUE) expect_error(nl.opts(opts2), "Argument `optlist` must be a named list.", fixed = TRUE) opts2 <- opts opts2$algorithm <- "NLOPT_LN_NELDERMEAD" expect_warning(nl.opts(opts2), "Option `algorithm` cannot be set here. It will be overwritten.", fixed = TRUE) expect_null(suppressWarnings(nl.opts(opts2)$algorithm)) nloptr/inst/tinytest/test-options-maxtime.R0000644000176200001440000000212614472716401020674 0ustar liggesusers# Copyright (C) 2015 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-options-maxtime.R # Author: Jelmer Ypma # Date: 22 March 2015 # # Maintenance assumed by Avraham Adler (AA) on 2023-02-10 # # Check whether the solver stop when maxtime # (set in the options) is reached. # CHANGELOG: # 2019-12-12: Corrected warnings and using updated testtthat framework (AA) # 2023-02-07: Remove wrapping tests in "test_that" to reduce duplication. (AA) library(nloptr) # Test that solver stops when maxtime is reached. # Objective function with sleep added such that maxtime will be reached when # solving the optimization problem. # eval_f <- function(x) { Sys.sleep(0.1) x ^ 2 } eval_grad_f <- function(x) 2 * x # Initial values. x0 <- 5 # Define optimizer options. opts <- list("algorithm" = "NLOPT_LD_LBFGS", "maxtime" = 0.05, "xtol_rel" = 1e-4) # Solve problem. res <- nloptr( x0 = x0, eval_f = eval_f, eval_grad_f = eval_grad_f, opts = opts ) # Check results. expect_identical(res$status, 6L) nloptr/inst/tinytest/test-hs023.R0000644000176200001440000000456414472716401016406 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-hs023.R # Author: Jelmer Ypma # Date: 16 August 2010 # # Maintenance assumed by Avraham Adler (AA) on 2023-02-10 # # Example problem, number 23 from the Hock-Schittkowsky test suite.. # # \min_{x} x1^2 + x2^2 # s.t. # x1 + x2 >= 1 # x1^2 + x2^2 >= 1 # 9*x1^2 + x2^2 >= 9 # x1^2 - x2 >= 0 # x2^2 - x1 >= 0 # # with bounds on the variables # -50 <= x1, x2 <= 50 # # we re-write the inequalities as # 1 - x1 - x2 <= 0 # 1 - x1^2 - x2^2 <= 0 # 9 - 9*x1^2 - x2^2 <= 0 # x2 - x1^2 <= 0 # x1 - x2^2 <= 0 # # the initial value is # x0 = (3, 1) # # Optimal solution = (1, 1) # # CHANGELOG: # 2014-05-05: Changed example to use unit testing framework testthat. # 2019-12-12: Corrected warnings and using updated testtthat framework (AA) # 2023-02-07: Remove wrapping tests in "test_that" to reduce duplication. (AA) # library(nloptr) # f(x) = x1^2 + x2^2 eval_f <- function(x) { list("objective" = x[1] ^ 2 + x[2] ^ 2, "gradient" = c(2 * x[1], 2 * x[2])) } # Inequality constraints. eval_g_ineq <- function(x) { constr <- c(1 - x[1] - x[2], 1 - x[1] ^ 2 - x[2] ^ 2, 9 - 9 * x[1] ^ 2 - x[2] ^ 2, x[2] - x[1] ^ 2, x[1] - x[2] ^ 2) grad <- rbind(c(-1, -1), c(-2 * x[1], -2 * x[2]), c(-18 * x[1], -2 * x[2]), c(-2 * x[1], 1), c(1, -2 * x[2])) list("constraints" = constr, "jacobian" = grad) } # Initial values. x0 <- c(3, 1) # Lower and upper bounds of control. lb <- c(-50, -50) ub <- c(50, 50) # Optimal solution. solution.opt <- c(1, 1) # Solve with MMA. opts <- list("algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1.0e-6, "tol_constraints_ineq" = rep(1.0e-6, 5), "print_level" = 0) res <- nloptr( x0 = x0, eval_f = eval_f, lb = lb, ub = ub, eval_g_ineq = eval_g_ineq, opts = opts ) # Run some checks on the optimal solution. expect_equal(res$solution, solution.opt, tolerance = 1e-6) expect_true(all(res$solution >= lb)) expect_true(all(res$solution <= ub)) # Check whether constraints are violated (up to specified tolerance). expect_true( all(eval_g_ineq(res$solution)$constr <= res$options$tol_constraints_ineq) ) nloptr/inst/tinytest/test-parameters.R0000644000176200001440000000310114472716401017674 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-parameters.R # Author: Jelmer Ypma # Date: 17 August 2010 # # Maintenance assumed by Avraham Adler (AA) on 2023-02-10 # # Example shows how we can have an objective function # depend on parameters or data. The objective function # is a simple polynomial. # # CHANGELOG: # 2014-05-05: Changed example to use unit testing framework testthat. # 2019-12-12: Corrected warnings and using updated testtthat framework (AA) # 2023-02-07: Remove wrapping tests in "test_that" to reduce duplication. (AA) # library(nloptr) # Test simple polyonmial where parameters are supplied as additional data. # Objective function and gradient in terms of parameters. eval_f <- function(x, params) { params[1] * x ^ 2 + params[2] * x + params[3] } eval_grad_f <- function(x, params) { 2 * params[1] * x + params[2] } # Define parameters that we want to use. params <- c(1, 2, 3) # Define initial value of the optimization problem. x0 <- 0 # Solve using nloptr adding params as an additional parameter res <- nloptr( x0 = x0, eval_f = eval_f, eval_grad_f = eval_grad_f, opts = list("algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1e-6), params = params ) # Solve using algebra # Minimize f(x) = ax^2 + bx + c. # Optimal value for control is -b/(2a). expect_equal(res$solution, -params[2] / (2 * params[1]), tolerance = 1e-7) # With value of the objective function f(-b/(2a)). expect_equivalent(res$objective, eval_f(-params[2] / (2 * params[1]), params)) nloptr/inst/tinytest/test-print.nloptr.R0000644000176200001440000000272514472716401020215 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-print.nloptr # Author: Avraham Adler # Date: 9 February 2023 # # Test code in print.nloptr function that is not tested elsewhere. # # Changelog: # 2023-08-23: Convert _output to _stdout for tinytest # library(nloptr) options(digits=7) x0 <- c(3, 3) fn <- function(x) (x[1] - 1) ^ 2 + (x[2] - 1) ^ 2 # Successful convergence (very loose tolerance so converges < 100) fit <- nloptr(x0, fn, opts = list(algorithm = "NLOPT_LN_NELDERMEAD", xtol_rel = 1e-2)) expect_stdout(print(fit), "Optimal value of controls: 1.004579 1.003978", fixed = TRUE) expect_stdout(print(fit, 1), "Optimal value of user-defined subset of controls: 1.004579", fixed = TRUE) expect_stdout(print(fit, 2), "Optimal value of user-defined subset of controls: 1.003978", fixed = TRUE) # Unsuccessful convergence (hit maxeval in this case) fit <- nloptr(x0, fn, opts = list(algorithm = "NLOPT_LN_NELDERMEAD", xtol_rel = 1e-8)) expect_stdout(print(fit), "Current value of controls: 0.9999994 1.000001", fixed = TRUE) expect_stdout(print(fit, 1), "Current value of user-defined subset of controls: 0.9999994", fixed = TRUE) expect_stdout(print(fit, 2), "Current value of user-defined subset of controls: 1.000001", fixed = TRUE) nloptr/inst/tinytest/test-wrapper-global.R0000644000176200001440000002216714760162227020465 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-global # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls to StoGo, ISRES, and CRS algorithms. As many of these # algorithms have issues, this test suite may not be completed. # # Changelog: # 2023-08-23: Change _output to _stdout. (Avraham Adler) # 2023-06-24: Reduce tolerance of ISRES tests to pass CRAN. (Aymeric Stamm) # 2023-06-25: Use analytic gradients and Jacobians for hin/heq. Correct some # of the ISRES tests which were pulling on Stogo results. # (Avraham Adler) # library(nloptr) tol <- 1e-3 # Stochastic algorithms require a weaker tolerance depMess <- paste("The old behavior for hin >= 0 has been deprecated. Please", "restate the inequality to be <=0. The ability to use the old", "behavior will be removed in a future release.") ## Functions for the algorithms rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2} ## Analytic gradient gr <- function(x) {c(-2 * (1 - x[1]) - 400 * x[1] * (x[2] - x[1] ^ 2), 200 * (x[2] - x[1] ^ 2))} gr.diff <- function(x) nl.grad(x, rbf) hin <- function(x) 0.25 * x[1L] ^ 2 + x[2L] ^ 2 - 1 # hin <= 0 heq <- function(x) x[1L] + x[2L] - 1 # heq = 0 hinjac <- function(x) c(0.5 * x[1L], 2 * x[2L]) heqjac <- function(x) c(1, 1) hin2 <- function(x) -hin(x) # Needed to test old behavior hinjac2 <- function(x) -hinjac(x) x0 <- c(-1.2, 1) lb <- c(-3, -3) ub <- c(3, 3) ## StoGo # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(stogo(x0, rbf, lower = lb, upper = ub, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(stogo(x0, rbf, lower = lb, upper = ub)) # No passed gradient; Randomized: FALSE stogoTest <- stogo(x0, rbf, lower = lb, upper = ub) stogoControl <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = gr.diff, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GD_STOGO", xtol_rel = 1e-6, maxeval = 10000L)) expect_identical(stogoTest$par, stogoControl$solution) expect_identical(stogoTest$value, stogoControl$objective) expect_identical(stogoTest$iter, stogoControl$iterations) expect_identical(stogoTest$convergence, stogoControl$status) expect_identical(stogoTest$message, stogoControl$message) # Passed gradient; Randomized: FALSE stogoTest <- stogo(x0, rbf, gr, lb, ub) stogoControl <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = gr, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GD_STOGO", xtol_rel = 1e-6, maxeval = 10000L)) expect_identical(stogoTest$par, stogoControl$solution) expect_identical(stogoTest$value, stogoControl$objective) expect_identical(stogoTest$iter, stogoControl$iterations) expect_identical(stogoTest$convergence, stogoControl$status) expect_identical(stogoTest$message, stogoControl$message) # Passed gradient; Randomized: TRUE stogoTest <- stogo(x0, rbf, gr, lb, ub, randomized = TRUE) stogoControl <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = gr, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GD_STOGO_RAND", xtol_rel = 1e-6, maxeval = 10000L)) expect_identical(stogoTest$par, stogoControl$solution) expect_identical(stogoTest$value, stogoControl$objective) expect_identical(stogoTest$iter, stogoControl$iterations) expect_identical(stogoTest$convergence, stogoControl$status) expect_identical(stogoTest$message, stogoControl$message) ## ISRES # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(isres(x0, rbf, lb, ub, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(isres(x0, rbf, lb, ub)) # As ISRES is stochastic, more iterations and a much looser tolerance is needed. # Also, iteration count will almost surely not be equal. # No passed hin or heq isresTest <- isres(x0, rbf, lb, ub, maxeval = 2e4L) isresControl <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GN_ISRES", maxeval = 2e4L, xtol_rel = 1e-6, population = 60)) expect_equal(isresTest$par, isresControl$solution, tolerance = tol) expect_equal(isresTest$value, isresControl$objective, tolerance = tol) expect_identical(isresTest$convergence, isresControl$status) expect_identical(isresTest$message, isresControl$message) # Passing heq # Cannot check for value equivalence since the stochastic nature of the problem # creates different solutions to this "improper" test even using the same seed # and calls! So dropping maxeval to 1e4 for speed. # (AA: 2024-06-25) isresTest <- isres(x0, rbf, lb, ub, heq = heq, maxeval = 1e4L) isresControl <- nloptr(x0 = x0, eval_f = rbf, eval_g_eq = heq, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GN_ISRES", maxeval = 1e4L, xtol_rel = 1e-6, population = 60)) expect_identical(isresTest$convergence, isresControl$status) expect_identical(isresTest$message, isresControl$message) # Passing hin isresControl <- nloptr(x0 = x0, eval_f = rbf, eval_g_ineq = hin, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GN_ISRES", maxeval = 2e4L, xtol_rel = 1e-6, population = 60)) expect_silent(isres(x0, rbf, lb, ub, hin = hin, maxeval = 2e4L, deprecatedBehavior = FALSE)) isresTest <- isres(x0, rbf, lb, ub, hin = hin, maxeval = 2e4L, deprecatedBehavior = FALSE) expect_equal(isresTest$par, isresControl$solution, tolerance = tol) expect_equal(isresTest$value, isresControl$objective, tolerance = tol) expect_identical(isresTest$convergence, isresControl$status) expect_identical(isresTest$message, isresControl$message) # Test deprecated message expect_warning(isres(x0, rbf, lower = lb, upper = ub, hin = hin2, maxeval = 2e4L), depMess) # Test deprecated behavior isresTest <- suppressWarnings(isres(x0, rbf, lb, ub, hin = hin2, maxeval = 2e4L)) expect_equal(isresTest$par, isresControl$solution, tolerance = tol) expect_equal(isresTest$value, isresControl$objective, tolerance = tol) expect_identical(isresTest$convergence, isresControl$status) expect_identical(isresTest$message, isresControl$message) ## CRS2LM # Take these outside the function since they are unchanging; just pass them! a <- c(1.0, 1.2, 3.0, 3.2) A <- matrix(c(10, 0.05, 3, 17, 3, 10, 3.5, 8, 17, 17, 1.7, 0.05, 3.5, 0.1, 10, 10, 1.7, 8, 17, 0.1, 8, 14, 8, 14), nrow = 4) B <- matrix(c(0.1312, 0.2329, 0.2348, 0.4047, 0.1696, 0.4135, 0.1451, 0.8828, 0.5569, 0.8307, 0.3522, 0.8732, 0.0124, 0.3736, 0.2883, 0.5743, 0.8283, 0.1004, 0.3047, 0.1091, 0.5886, 0.9991, 0.6650, 0.0381), nrow = 4) hartmann6 <- function(x, a, A, B) { fun <- 0 for (i in 1:4) { fun <- fun - a[i] * exp(-sum(A[i, ] * (x - B[i, ]) ^ 2)) } fun } # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. x0 <- lb <- rep(0, 6L) ub <- rep(1, 6L) expect_stdout(crs2lm(x0 = x0, hartmann6, lower = lb, upper = ub, nl.info = TRUE, a = a, A = A, B = B), "Call:", fixed = TRUE) expect_silent(crs2lm(x0 = x0, hartmann6, lower = lb, upper = ub, a = a, A = A, B = B)) crs2lmTest <- crs2lm(x0 = x0, hartmann6, lower = lb, upper = ub, ranseed = 43L, xtol_rel = 1e-8, maxeval = 100L, a = a, A = A, B = B) crs2lmControl <- nloptr(x0 = x0, eval_f = hartmann6, lb = lb, ub = ub, a = a, A = A, B = B, opts = list(algorithm = "NLOPT_GN_CRS2_LM", xtol_rel = 1e-8, maxeval = 100L, ranseed = 43L, population = 70)) expect_identical(crs2lmTest$par, crs2lmControl$solution) expect_identical(crs2lmTest$value, crs2lmControl$objective) expect_identical(crs2lmTest$iter, crs2lmControl$iterations) expect_identical(crs2lmTest$convergence, crs2lmControl$status) expect_identical(crs2lmTest$message, crs2lmControl$message) nloptr/inst/tinytest/test-wrapper-mma.R0000644000176200001440000001076014633255630017773 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-mma # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls to MMA algorithm # # CHANGELOG # # 2023-08-23: Change _output to _stdout # 2024-06-04: Switched desired direction of the hin/hinjac inequalities, leaving # the old behavior as the default for now. Also cleaned up the HS100 # example. (Avraham Adler) library(nloptr) depMess <- paste("The old behavior for hin >= 0 has been deprecated. Please", "restate the inequality to be <=0. The ability to use the old", "behavior will be removed in a future release.") # Taken from example x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} hin.hs100 <- function(x) {c( 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - 11 * x[7]) } gr.hs100 <- function(x) { c( 2 * x[1] - 20, 10 * x[2] - 120, 4 * x[3] ^ 3, 6 * x[4] - 66, 60 * x[5] ^ 5, 14 * x[6] - 4 * x[7] - 10, 4 * x[7] ^ 3 - 4 * x[6] - 8) } hinjac.hs100 <- function(x) { matrix(c(4 * x[1], 12 * x[2] ^ 3, 1, 8 * x[4], 5, 0, 0, 7, 3, 20 * x[3], 1, -1, 0, 0, 23, 2 * x[2], 0, 0, 0, 12 * x[6], -8, 8 * x[1] - 3 * x[2], 2 * x[2] - 3 * x[1], 4 * x[3], 0, 0, 5, -11), nrow = 4, byrow = TRUE) } hin2.hs100 <- function(x) -hin.hs100(x) # Needed to test old behavior hinjac2.hs100 <- function(x) -hinjac.hs100(x) # Needed to test old behavior ctl <- list(xtol_rel = 1e-8) # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(suppressMessages(mma(x0.hs100, fn.hs100, nl.info = TRUE)), "Call:", fixed = TRUE) # Expect unconstrained call to work expect_silent(mma(x0.hs100, fn.hs100)) # Test MMA algorithm with inequality but passing neither gradient nor Jacobian. # As everyone is on Windows64, timing should be less of an issue. mmaTest <- mma(x0.hs100, fn.hs100, hin = hin.hs100, control = ctl, deprecatedBehavior = FALSE) mmaControl <- nloptr(x0 = x0.hs100, eval_f = fn.hs100, eval_grad_f = function(x) nl.grad(x, fn.hs100), eval_g_ineq = hin.hs100, eval_jac_g_ineq = function(x) nl.jacobian(x, hin.hs100), opts = list(algorithm = "NLOPT_LD_MMA", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(mmaTest$par, mmaControl$solution) expect_identical(mmaTest$value, mmaControl$objective) expect_identical(mmaTest$iter, mmaControl$iterations) expect_identical(mmaTest$convergence, mmaControl$status) expect_identical(mmaTest$message, mmaControl$message) # Test MMA algorithm passing both gradient and Jacobian. Now correct. # (AA: 2024-06-04) mmaControl <- nloptr(x0 = x0.hs100, eval_f = fn.hs100, eval_grad_f = gr.hs100, eval_g_ineq = hin.hs100, eval_jac_g_ineq = hinjac.hs100, opts = list(algorithm = "NLOPT_LD_MMA", xtol_rel = 1e-8, maxeval = 1000L)) mmaTest <- mma(x0.hs100, fn.hs100, gr = gr.hs100, hin = hin.hs100, hinjac = hinjac.hs100, control = ctl, deprecatedBehavior = FALSE) expect_identical(mmaTest$par, mmaControl$solution) expect_identical(mmaTest$value, mmaControl$objective) expect_identical(mmaTest$iter, mmaControl$iterations) expect_identical(mmaTest$convergence, mmaControl$status) expect_identical(mmaTest$message, mmaControl$message) # Test deprecated message expect_warning(mma(x0.hs100, fn.hs100, hin = hin.hs100), depMess) # Test deprecated behavior mmaTest <- suppressWarnings(mma(x0.hs100, fn.hs100, gr = gr.hs100, hin = hin2.hs100, hinjac = hinjac2.hs100, control = ctl)) expect_identical(mmaTest$par, mmaControl$solution) expect_identical(mmaTest$value, mmaControl$objective) expect_identical(mmaTest$iter, mmaControl$iterations) expect_identical(mmaTest$convergence, mmaControl$status) expect_identical(mmaTest$message, mmaControl$message) nloptr/inst/tinytest/test-nloptr.R0000644000176200001440000002453014765064402017062 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-nloptr # Author: Avraham Adler # Date: 7 February 2023 # # Test code in nloptr.R and nloptr.c which is not tested elsewhere. # # Changelog: # 2023-08-23: Converted snapshots to testing portions of outputs and messages. # # It is possible for NLOPT to go slightly beyond maxtime or maxeval, especially # for the global algorithms, which is why the stopping criterion has a # weird-looking test. See # https://nlopt.readthedocs.io/en/latest/NLopt_Reference/#stopping-criteria library(nloptr) options(digits = 7) tol <- sqrt(.Machine$double.eps) ########################## Tests for nloptr.R ################################## ctlNM <- list(algorithm = "NLOPT_LN_NELDERMEAD", xtol_rel = 1e-8, check_derivatives = FALSE) # check x0 expect_error(nloptr("3", function(x) x, opts = ctlNM), "x0 must be numeric", fixed = TRUE) expect_error(nloptr(numeric(), function(x) x, opts = ctlNM), "x0 must have length > 0", fixed = TRUE) ctlNM <- list(algorithm = "NLOPT_LN_NELDERMEAD", xtol_rel = 1e-8, check_derivatives = TRUE) ctlSQP <- list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8, check_derivatives = TRUE) # internal function to check the arguments of the functions expect_error(nloptr(3, "Zed"), "must be a function", fixed = TRUE) fn <- function(x, b = NULL, c = NULL) x expect_error(nloptr(3, fn, c = "Q"), "but this has not been passed to the 'nloptr' function", fixed = TRUE) expect_error(nloptr(3, fn, b = "X", c = "Y", d = "Q"), "passed to (...) in 'nloptr' but this is not required in the", fixed = TRUE) expect_warning(nloptr(3, fn, b = 3, c = 4, opts = ctlNM), "Skipping derivative checker because algorithm", fixed = TRUE) ########################## Tests for nloptr.c ################################## ctl <- list(xtol_rel = 1e-8, maxeval = 1000L) fn <- function(x) x ^ 2 - 4 * x + 4 lb <- 0 ub <- 6 optSol <- 2 optVal <- 0 ## NLOPT_GN_DIRECT_L_NOSCAL alg <- list(algorithm = "NLOPT_GN_DIRECT_L_NOSCAL") testRun <- nloptr(5, fn, lb = lb, ub = ub, opts = c(alg, ctl)) expect_equal(testRun$solution, optSol, tolerance = tol) expect_equal(testRun$objective, optVal, tolerance = tol) expect_true(testRun$iterations <= ctl$maxeval + 5) expect_true(testRun$status > 0) ## NLOPT_GN_DIRECT_L_RAND_NOSCAL alg <- list(algorithm = "NLOPT_GN_DIRECT_L_RAND_NOSCAL") testRun <- nloptr(5, fn, lb = lb, ub = ub, opts = c(alg, ctl)) expect_equal(testRun$solution, optSol, tolerance = tol) expect_equal(testRun$objective, optVal, tolerance = tol) expect_true(testRun$iterations <= ctl$maxeval + 5) expect_true(testRun$status > 0) ## NLOPT_LN_PRAXIS alg <- list(algorithm = "NLOPT_LN_PRAXIS") testRun <- nloptr(5, fn, lb = lb, ub = ub, opts = c(alg, ctl)) expect_equal(testRun$solution, optSol, tolerance = tol) expect_equal(testRun$objective, optVal, tolerance = tol) expect_true(testRun$iterations <= ctl$maxeval + 5) expect_true(testRun$status > 0) ## NLOPT_GN_MLSL alg <- list(algorithm = "NLOPT_GN_MLSL") lopts <- list(local_opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-8)) testRun <- nloptr(5, fn, lb = lb, ub = ub, opts = c(alg, ctl, lopts)) expect_equal(testRun$solution, optSol, tolerance = tol) expect_equal(testRun$objective, optVal, tolerance = tol) expect_true(testRun$iterations <= ctl$maxeval + 5) expect_true(testRun$status > 0) ## NLOPT_GN_MLSL_LDS alg <- list(algorithm = "NLOPT_GN_MLSL_LDS") lopts <- list(local_opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-8)) testRun <- nloptr(5, fn, lb = lb, ub = ub, opts = c(alg, ctl, lopts)) expect_equal(testRun$solution, optSol, tolerance = tol) expect_equal(testRun$objective, optVal, tolerance = tol) expect_true(testRun$iterations <= ctl$maxeval + 5) expect_true(testRun$status > 0) ## NLOPT_LN_AUGLAG_EQ x0 <- c(-2, 2, 2, -1, -1) fn1 <- function(x) exp(x[1] * x[2] * x[3] * x[4] * x[5]) eqn1 <- function(x) { c(x[1] * x[1] + x[2] * x[2] + x[3] * x[3] + x[4] * x[4] + x[5] * x[5], x[2] * x[3] - 5 * x[4] * x[5], x[1] * x[1] * x[1] + x[2] * x[2] * x[2]) } optSol <- rep(0, 5) optVal <- 1 testRun <- nloptr(x0, fn1, eval_g_eq = eqn1, opts = list(algorithm = "NLOPT_LN_AUGLAG_EQ", xtol_rel = 1e-6, maxeval = 10000L, local_opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-6, maxeval = 1000L))) expect_equal(testRun$solution, optSol, tolerance = tol) expect_equal(testRun$objective, optVal, tolerance = tol) expect_true(testRun$iterations <= 10005L) expect_true(testRun$status > 0) ## NLOPT_LD_AUGLAG_EQ gr1 <- function(x) { c(x[2] * x[3] * x[4] * x[5], x[1] * x[3] * x[4] * x[5], x[1] * x[2] * x[4] * x[5], x[1] * x[2] * x[3] * x[5], x[1] * x[2] * x[3] * x[4]) * exp(prod(x)) } heqjac <- function(x) nl.jacobian(x0, eqn1) testRun <- nloptr(x0, fn1, gr1, eval_g_eq = eqn1, eval_jac_g_eq = heqjac, opts = list(algorithm = "NLOPT_LD_AUGLAG_EQ", xtol_rel = 1e-6, maxeval = 10000L, local_opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-6, maxeval = 1000L))) expect_equal(testRun$solution, optSol, tolerance = tol) expect_equal(testRun$objective, optVal, tolerance = tol) expect_true(testRun$iterations <= 10005L) expect_true(testRun$status > 0) # https://www.wolframalpha.com/input?i=minimum+of+x+%5E+4+%2B+y+%5E+2+-+5+*+x+*+y++%2B+5+ # nolint fn <- function(x) x[1L] ^ 4 + x[2L] ^ 2 - 5 * x[1L] * x[2L] + 5 gr <- function(x) c(4 * x[1L] ^ 3 - 5 * x[2L], 2 * x[2L] - 5 * x[1L]) lb <- c(0, 0) ub <- c(5, 5) optSol <- c(5 / (2 * sqrt(2)), 25 / (4 * sqrt(2))) optVal <- -305 / 64 ## TO DO: check why this is not working ## NLOPT_LN_NEWUOA_BOUND # alg <- list(algorithm = "NLOPT_LN_NEWUOA_BOUND") # testRun <- nloptr(c(1, 1), fn, lb = lb, ub = ub, opts = c(alg, ctl)) # # expect_equal(testRun$solution, optSol, tolerance = 1e-5) # expect_equal(testRun$objective, optVal, tolerance = tol) # expect_true(testRun$iterations <= ctl$maxeval + 5) # expect_true(testRun$status > 0) ## NLOPT_GN_ESCH alg <- list(algorithm = "NLOPT_GN_ESCH") ctl <- list(xtol_rel = 1e-8, maxeval = 50000L) testRun <- nloptr(c(1, 1), fn, lb = lb, ub = ub, opts = c(alg, ctl)) expect_equal(testRun$solution, optSol, tolerance = 1e-2) expect_equal(testRun$objective, optVal, tolerance = 1e-2) expect_true(testRun$iterations <= ctl$maxeval + 5) expect_true(testRun$status > 0) if (nloptr:::have.nlopt.ld.lbfgs.nocedal) { ## NLOPT_LD_LBFGS_NOCEDAL # NLOPT_LD_LBFGS_NOCEDAL as this algorithm has not been included as of NLOPT # 2.7.1 per https://github.com/stevengj/nlopt/issues/40 so the expected outcome # is NLOPT_INVALID_ARGS. Perhaps we should ring-fence it for now? # (AA: 2023-02-08) alg <- list(algorithm = "NLOPT_LD_LBFGS_NOCEDAL") testRun <- nloptr(c(1, 1), fn, gr, lb = lb, ub = ub, opts = c(alg, ctl)) minus2mess <- paste("NLOPT_INVALID_ARGS: Invalid arguments (e.g. lower bounds", "are bigger than upper bounds, an unknown algorithm was", "specified, etcetera).") expect_identical(testRun$status, -2L) expect_identical(testRun$message, minus2mess) } ## case NLOPT_FAILURE fnl <- function(x) { list(objective = (x[1] - 1) ^ 2 + (x[2] - 1) ^ 2, gradient = c(4 * (x[1] - 1), 3 - (x[2] - 1))) } x0 <- c(3, 3) testRun <- nloptr(x0, fnl, opts = list(algorithm = "NLOPT_LD_LBFGS", xtol_rel = 1e-8)) expect_identical(testRun$status, -1L) expect_identical(testRun$message, "NLOPT_FAILURE: Generic failure code.") # Tinytest has no snapshot functionality. Instead, this will test the output # and message against portions of the expected, instead of the totality. ## MULTIVARIATE FUNCTION x0 <- c(2, 2) ub <- c(5, 5) lb <- c(-1, -1) fn <- function(x) (x[1L] - 1) ^ 2 + (x[2L] - 1) ^ 2 + 1 gr <- function(x) c(2 * (x[1L] - 1), 2 * (x[2L] - 1)) hin <- function(x) c(1.44 - x[1L] ^ 2, 2.197 - x[2L] ^ 3) hinjac <- function(x) matrix(c(-2 * x[1L], 0, 0, -3 * x[2L] ^ 2), 2L, 2L) heq <- function(x) c(x[1L] * x[2L] - 2.55, x[1L] - x[2L] - 0.2) heqjac <- function(x) matrix(c(x[2L], 1, x[1L], -1), 2L) optSol <- c(1.7, 1.5) optVal <- 1.74 expect_stdout( suppressMessages( nloptr(x0, fn, gr, lb, ub, hin, hinjac, heq, heqjac, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8, print_level = 3, check_derivatives = TRUE)) ), "g(x) = (-1.450000, -1.178000)", fixed = TRUE ) # Wrap in capture.output to prevent wall of text on screen when running. This is # to test the message; expect_stdout tests the output. expect_message( capture.output( nloptr(x0, fn, gr, lb, ub, hin, hinjac, heq, heqjac, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8, print_level = 3, check_derivatives = TRUE)), type = "output" ), "eval_jac_g_ineq[1, 1] = -4.0e+00 ~ -4.0e+00 [7.450581e-09]", fixed = TRUE ) ## UNIVARIATE FUNCTION x0 <- 5 fn <- function(x) x ^ 2 - 4 * x + 4 gr <- function(x) 2 * x - 4 hin <- function(x) 5.29 - x ^ 2 hinjac <- function(x) -2 * x heq <- function(x) 10 * x - 27 heqjac <- function(x) 10 lb <- 0 ub <- 6 optSol <- 2.7 optVal <- 0.49 ## UNIVARIATE expect_stdout( suppressMessages( nloptr(x0, fn, gr, lb, ub, hin, hinjac, heq, heqjac, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8, print_level = 3, check_derivatives = TRUE)) ), "g(x) = -2.000000", fixed = TRUE ) expect_message( capture.output( nloptr(x0, fn, gr, lb, ub, hin, hinjac, heq, heqjac, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8, print_level = 3, check_derivatives = TRUE)), type = "output" ), "eval_jac_g_ineq[1] = -1e+01 ~ -1e+01 [9.536743e-09]", fixed = TRUE ) # Test NLOPT_ROUNDOFF_LIMITED expect_true( grepl("Roundoff errors led to a breakdown", nloptr(x0, fn, gr, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = -Inf))$message, fixed = TRUE) ) # Test triggering stopval expect_true( grepl("Optimization stopped because stopval", nloptr(c(4, 4), fn, opts = list(algorithm = "NLOPT_LN_SBPLX", stopval = 20))$message, fixed = TRUE) ) nloptr/inst/tinytest/test-example.R0000644000176200001440000000701314472716401017172 0ustar liggesusers# Copyright (C) 2010-14 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-example.R # Author: Jelmer Ypma # Date: 10 June 2010 # # Maintenance assumed by Avraham Adler (AA) on 2023-02-10 # # Example showing how to solve the problem from the NLopt tutorial. # # min sqrt(x2) # s.t. x2 >= 0 # x2 >= (a1*x1 + b1)^3 # x2 >= (a2*x1 + b2)^3 # where # a1 = 2, b1 = 0, a2 = -1, b2 = 1 # # re-formulate constraints to be of form g(x) <= 0 # (a1*x1 + b1)^3 - x2 <= 0 # (a2*x1 + b2)^3 - x2 <= 0 # # Optimal solution: (1/3, 8/27) # # CHANGELOG: # 2014-05-03: Changed example to use unit testing framework testthat. # 2019-12-12: Corrected warnings and using updated testtthat framework (AA) # 2023-02-07: Remove wrapping tests in "test_that" to reduce duplication. (AA) library(nloptr) tol <- sqrt(.Machine$double.eps) # objective function eval_f0 <- function(x, a, b) sqrt(x[2]) # constraint function eval_g0 <- function(x, a, b) (a * x[1] + b) ^ 3 - x[2] # gradient of objective function eval_grad_f0 <- function(x, a, b) c(0, 0.5 / sqrt(x[2])) # jacobian of constraint eval_jac_g0 <- function(x, a, b) { rbind(c(3 * a[1] * (a[1] * x[1] + b[1]) ^ 2, -1), c(3 * a[2] * (a[2] * x[1] + b[2]) ^ 2, -1)) } # Functions with gradients in objective and constraint function. This can be # useful if the same calculations are needed for the function value and the # gradient. eval_f1 <- function(x, a, b) { list("objective" = sqrt(x[2]), "gradient" = c(0, 0.5 / sqrt(x[2]))) } eval_g1 <- function(x, a, b) { list("constraints" = (a * x[1] + b) ^ 3 - x[2], "jacobian" = rbind(c(3 * a[1] * (a[1] * x[1] + b[1]) ^ 2, -1), c(3 * a[2] * (a[2] * x[1] + b[2]) ^ 2, -1))) } # Define parameters. a <- c(2, -1) b <- c(0, 1) # Define optimal solution. solution.opt <- c(1 / 3, 8 / 27) # Test NLopt tutorial example with NLOPT_LD_MMA with gradient information. Solve # using NLOPT_LD_MMA with gradient information supplied in separate function. res0 <- nloptr( x0 = c(1.234, 5.678), eval_f = eval_f0, eval_grad_f = eval_grad_f0, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g0, eval_jac_g_ineq = eval_jac_g0, opts = list("xtol_rel" = 1e-4, "algorithm" = "NLOPT_LD_MMA"), a = a, b = b ) expect_equal(res0$solution, solution.opt, tolerance = tol) # Test NLopt tutorial example with NLOPT_LN_COBYLA with gradient information. # Solve using NLOPT_LN_COBYLA without gradient information A tighter convergence # tolerance is used here (1e-6), to ensure that the final solution is equal to # the optimal solution (within some tolerance). res1 <- nloptr( x0 = c(1.234, 5.678), eval_f = eval_f0, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g0, opts = list("xtol_rel" = 1e-6, "algorithm" = "NLOPT_LN_COBYLA"), a = a, b = b ) expect_equal(res1$solution, solution.opt, tolerance = tol) # Test NLopt tutorial example with NLOPT_LN_COBYLA with gradient information # using combined function. # Solve using NLOPT_LD_MMA with gradient information in objective function res2 <- nloptr( x0 = c(1.234, 5.678), eval_f = eval_f1, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g1, opts = list("xtol_rel" = 1e-4, "algorithm" = "NLOPT_LD_MMA"), a = a, b = b ) expect_equal(res2$solution, solution.opt, tolerance = tol) nloptr/inst/tinytest/test-wrapper-direct.R0000644000176200001440000001432614472716401020474 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-direct # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls to DIRECT algorithms # # Changelog: # 2023-08-23: Change _output to _stdout # library(nloptr) # DirectL is not identical when calling randomized = TRUE. May be an issue with # the randomization at the C level. For now, need to pass this tolerance for it # to work. # (AA: 2026-02-06) tol <- 1e-6 ## Functions for DIRECT and DIRECT_L hartmann6 <- function(x) { a <- c(1, 1.2, 3, 3.2) A <- matrix(c(10, 0.05, 3, 17, 3, 10, 3.5, 8, 17, 17, 1.7, 0.05, 3.5, 0.1, 10, 10, 1.7, 8, 17, 0.1, 8, 14, 8, 14), nrow = 4L, ncol = 6L) B <- matrix(c(0.1312, 0.2329, 0.2348, 0.4047, 0.1696, 0.4135, 0.1451, 0.8828, 0.5569, 0.8307, 0.3522, 0.8732, 0.0124, 0.3736, 0.2883, 0.5743, 0.8283, 0.1004, 0.3047, 0.1091, 0.5886, 0.9991, 0.6650, 0.0381), nrow = 4L, ncol = 6L) fun <- 0 for (i in 1:4) { fun <- fun - a[i] * exp(-sum(A[i, ] * (x - B[i, ]) ^ 2)) } fun } lb <- rep(0, 6L) ub <- rep(1, 6L) x0 <- rep(0.5, 6L) ctl <- list(xtol_rel = 1e-8, maxeval = 1000L) # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(direct(hartmann6, lb, ub, nl.info = TRUE), "Call:", fixed = TRUE) expect_stdout(directL(hartmann6, lb, ub, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(direct(hartmann6, lb, ub)) expect_silent(directL(hartmann6, lb, ub)) # Test DIRECT algorithm Scaled: TRUE Original: FALSE directTest <- direct(hartmann6, lb, ub, control = ctl) directControl <- nloptr(x0 = x0, eval_f = hartmann6, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GN_DIRECT", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(directTest$par, directControl$solution) expect_identical(directTest$value, directControl$objective) expect_identical(directTest$iter, directControl$iterations) expect_identical(directTest$convergence, directControl$status) expect_identical(directTest$message, directControl$message) # Test DIRECT algorithm Scaled: FALSE Original: FALSE directTest <- direct(hartmann6, lb, ub, scaled = FALSE, control = ctl) directControl <- nloptr(x0 = x0, eval_f = hartmann6, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GN_DIRECT_NOSCAL", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(directTest$par, directControl$solution) expect_identical(directTest$value, directControl$objective) expect_identical(directTest$iter, directControl$iterations) expect_identical(directTest$convergence, directControl$status) expect_identical(directTest$message, directControl$message) # Test DIRECT algorithm Original: TRUE directTest <- direct(hartmann6, lb, ub, scaled = FALSE, original = TRUE, control = ctl) directControl <- nloptr(x0 = x0, eval_f = hartmann6, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GN_ORIG_DIRECT", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(directTest$par, directControl$solution) expect_identical(directTest$value, directControl$objective) expect_identical(directTest$iter, directControl$iterations) expect_identical(directTest$convergence, directControl$status) expect_identical(directTest$message, directControl$message) # Test DIRECTL algorithm Randomized: FALSE Original: FALSE directLTest <- directL(hartmann6, lb, ub, control = ctl) directLControl <- nloptr(x0 = x0, eval_f = hartmann6, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GN_DIRECT_L", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(directLTest$par, directLControl$solution) expect_identical(directLTest$value, directLControl$objective) expect_identical(directLTest$iter, directLControl$iterations) expect_identical(directLTest$convergence, directLControl$status) expect_identical(directLTest$message, directLControl$message) # Test DIRECTL algorithm Original: TRUE ctl <- list(xtol_rel = 1e-8, maxeval = 10000L) directLTest <- directL(hartmann6, lb, ub, randomized = TRUE, original = TRUE, control = ctl) directLControl <- nloptr(x0 = x0, eval_f = hartmann6, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GN_ORIG_DIRECT_L", xtol_rel = 1e-8, maxeval = 10000L)) expect_identical(directLTest$par, directLControl$solution) expect_identical(directLTest$value, directLControl$objective) expect_identical(directLTest$iter, directLControl$iterations) expect_identical(directLTest$convergence, directLControl$status) expect_identical(directLTest$message, directLControl$message) # Test DIRECTL algorithm Randomized: TRUE Original: FALSE ctl <- list(xtol_rel = 1e-8, maxeval = 50000L) directLTest <- directL(hartmann6, lb, ub, randomized = TRUE, control = ctl) directLControl <- nloptr(x0 = x0, eval_f = hartmann6, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GN_DIRECT_L_RAND", xtol_rel = 1e-8, maxeval = 50000L)) # May have something to do with the randomization. Setting seeds before the # calls does not help with check_identical # (AA: 2023-02-06) expect_equal(directLTest$par, directLControl$solution, tolerance = tol) expect_equal(directLTest$value, directLControl$objective, tolerance = tol) expect_identical(directLTest$iter, directLControl$iterations) expect_identical(directLTest$convergence, directLControl$status) expect_identical(directLTest$message, directLControl$message) nloptr/inst/tinytest/test-wrapper-lbgfs.R0000644000176200001440000000453414472716401020317 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-lbgfs # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls to LBGFS # # Changelog: # 2023-08-23: Change _output to _stdout # library(nloptr) ## Functions for the algorithms flb <- function(x) { p <- length(x) sum(c(1, rep(4, p - 1)) * (x - c(1, x[-p]) ^ 2) ^ 2) } x0 <- rep(3, 25L) lb <- rep(2, 25L) ub <- rep(4, 25L) ctl <- list(xtol_rel = 1e-8) # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(lbfgs(x0, flb, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(lbfgs(x0, flb)) # No passed gradient lbfgsTest <- lbfgs(x0, flb, lower = lb, upper = ub, control = ctl) lbfgsControl <- nloptr(x0 = x0, eval_f = flb, eval_grad_f = function(x) nl.grad(x, flb), lb = lb, ub = ub, opts = list(algorithm = "NLOPT_LD_LBFGS", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(lbfgsTest$par, lbfgsControl$solution) expect_identical(lbfgsTest$value, lbfgsControl$objective) expect_identical(lbfgsTest$iter, lbfgsControl$iterations) expect_identical(lbfgsTest$convergence, lbfgsControl$status) expect_identical(lbfgsTest$message, lbfgsControl$message) # Passed gradient fr <- function(x) {100 * (x[2L] - x[1L] ^ 2) ^ 2 + (1 - x[1L]) ^ 2} gr <- function(x) { .expr2 <- x[2L] - x[1L] ^ 2 .expr5 <- 1 - x[1L] c(-(2 * .expr5 + 100 * (2 * (2 * x[1L] * .expr2))), 100 * (2 * .expr2)) } lbfgsTest <- lbfgs(c(-1.2, 2), fr, gr, lower = c(-3, -3), upper = c(3, 3), control = ctl) lbfgsControl <- nloptr(x0 = c(-1.2, 2), eval_f = fr, eval_grad_f = gr, lb = c(-3, -3), ub = c(3, 3), opts = list(algorithm = "NLOPT_LD_LBFGS", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(lbfgsTest$par, lbfgsControl$solution) expect_identical(lbfgsTest$value, lbfgsControl$objective) expect_identical(lbfgsTest$iter, lbfgsControl$iterations) expect_identical(lbfgsTest$convergence, lbfgsControl$status) expect_identical(lbfgsTest$message, lbfgsControl$message) nloptr/inst/tinytest/test-wrapper-varmetric.R0000644000176200001440000000560514472716401021216 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-varmetric # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls to Shifted limited-memory variable-metric algorithm. # # Changelog: # 2023-08-23: Change _output to _stdout # library(nloptr) ## Functions for the algorithms flb <- function(x) { p <- length(x) sum(c(1, rep(4, p - 1)) * (x - c(1, x[-p]) ^ 2) ^ 2) } x0 <- rep(3, 25L) lb <- rep(2, 25L) ub <- rep(4, 25L) ctl <- list(xtol_rel = 1e-8) # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(varmetric(x0, flb, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(varmetric(x0, flb)) # No passed gradient; Rank 1 varTest <- varmetric(x0, flb, lower = lb, upper = ub, control = ctl, rank2 = FALSE) varControl <- nloptr(x0 = x0, eval_f = flb, eval_grad_f = function(x) nl.grad(x, flb), lb = lb, ub = ub, opts = list(algorithm = "NLOPT_LD_VAR1", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(varTest$par, varControl$solution) expect_identical(varTest$value, varControl$objective) expect_identical(varTest$iter, varControl$iterations) expect_identical(varTest$convergence, varControl$status) expect_identical(varTest$message, varControl$message) # No passed gradient; Rank 2 varTest <- varmetric(x0, flb, lower = lb, upper = ub, control = ctl) varControl <- nloptr(x0 = x0, eval_f = flb, eval_grad_f = function(x) nl.grad(x, flb), lb = lb, ub = ub, opts = list(algorithm = "NLOPT_LD_VAR2", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(varTest$par, varControl$solution) expect_identical(varTest$value, varControl$objective) expect_identical(varTest$iter, varControl$iterations) expect_identical(varTest$convergence, varControl$status) expect_identical(varTest$message, varControl$message) # Passed gradient fr <- function(x) {100 * (x[2L] - x[1L] ^ 2) ^ 2 + (1 - x[1L]) ^ 2} gr <- function(x) { .expr2 <- x[2L] - x[1L] ^ 2 .expr5 <- 1 - x[1L] c(-(2 * .expr5 + 100 * (2 * (2 * x[1L] * .expr2))), 100 * (2 * .expr2)) } varTest <- varmetric(c(-1.2, 2), fr, gr, control = ctl) varControl <- nloptr(x0 = c(-1.2, 2), eval_f = fr, eval_grad_f = gr, opts = list(algorithm = "NLOPT_LD_VAR2", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(varTest$par, varControl$solution) expect_identical(varTest$value, varControl$objective) expect_identical(varTest$iter, varControl$iterations) expect_identical(varTest$convergence, varControl$status) expect_identical(varTest$message, varControl$message) nloptr/inst/tinytest/test-systemofeq.R0000644000176200001440000000526014472716401017740 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-systemofeq.R # Author: Jelmer Ypma # Date: 20 June 2010 # # Maintenance assumed by Avraham Adler (AA) on 2023-02-10 # # Example showing how to solve a system of equations. # # min 1 # s.t. x^2 + x - 1 = 0 # # Optimal solution for x: -1.61803398875 # # CHANGELOG: # 2011-06-16: added NLOPT_LD_SLSQP # 2014-05-05: Changed example to use unit testing framework testthat. # 2019-12-12: Corrected warnings and using updated testtthat framework (AA) # 2023-02-07: Remove wrapping tests in "test_that" to reduce duplication. (AA) library(nloptr) tol <- sqrt(.Machine$double.eps) # Test Solve system of equations using NLOPT_LD_MMA with local optimizer # NLOPT_LD_MMA. # Objective function. eval_f0 <- function(x, params) 1 # Gradient of objective function. eval_grad_f0 <- function(x, params) 0 # Equality constraint function. eval_g0_eq <- function(x, params) params[1] * x ^ 2 + params[2] * x + params[3] # Jacobian of constraint. eval_jac_g0_eq <- function(x, params) 2 * params[1] * x + params[2] # Define vector with addiitonal data. params <- c(1, 1, -1) # Define optimal solution. solution.opt <- -1.61803398875 local_opts <- list("algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1.0e-6) opts <- list("algorithm" = "NLOPT_LD_AUGLAG", "xtol_rel" = 1.0e-6, "local_opts" = local_opts) res <- nloptr(x0 = -5, eval_f = eval_f0, eval_grad_f = eval_grad_f0, eval_g_eq = eval_g0_eq, eval_jac_g_eq = eval_jac_g0_eq, opts = opts, params = params) # Run some checks on the optimal solution. expect_equal(res$solution, solution.opt, tolerance = tol) # Check whether constraints are violated (up to specified tolerance). expect_equal(eval_g0_eq(res$solution, params = params), 0, tolerance = res$options$tol_constraints_eq) # Test Solve system of equations using NLOPT_LD_SLSQP. # Solve using NLOPT_LD_SLSQP. opts <- list("algorithm" = "NLOPT_LD_SLSQP", "xtol_rel" = 1.0e-6) res <- nloptr(x0 = -5, eval_f = eval_f0, eval_grad_f = eval_grad_f0, eval_g_eq = eval_g0_eq, eval_jac_g_eq = eval_jac_g0_eq, opts = opts, params = params) # Run some checks on the optimal solution. expect_equal(res$solution, solution.opt, tolerance = tol) # Check whether constraints are violated (up to specified tolerance). expect_equal(eval_g0_eq(res$solution, params = params), 0, tolerance = res$options$tol_constraints_eq) nloptr/inst/tinytest/test-derivative-checker.R0000644000176200001440000000565214472716401021312 0ustar liggesusers# Copyright (C) 201 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-derivative-checker.R # Author: Jelmer Ypma # Date: 24 July 2010 # # Maintenance assumed by Avraham Adler (AA) on 2023-02-10 # # Example showing results of the derivative checker and finite-difference # # Changelog: # 2013-10-27: Changed example to use unit testing framework testthat. # 2019-12-12: Corrected warnings and using updated testtthat framework (AA) # 2023-02-10: Remove wrapping tests in "test_that" to reduce duplication. # and add explicit accuracy checks for nloptr:::finite.diff.R (AA) # 2023-08-23: Prefix finite.diff with nloptr::: as part of move to tinytest # library(nloptr) # Test derivative checker. tol <- 1e-7 # Define objective function. f <- function(x, a) sum((x - a) ^ 2) # Define gradient function without errors. f_grad <- function(x, a) 2 * (x - a) # Generated a using: # > set.seed(3141) # > a <- runif(10) # > dump("a", file = "") a <- c(0.75499595934525132, 0.9649918619543314, 0.041430773446336389, 0.42781219445168972, 0.65170943737030029, 0.83836922678165138, 0.77428539283573627, 0.53199269832111895, 0.76871572202071548, 0.7851746492087841) # Test nloptr:::finite.diff on multivariate scalar function expect_equal(nloptr:::finite.diff(f, 1:10, a = a), f_grad(1:10, a = a), tolerance = tol) expect_equal(nloptr:::finite.diff(f, 1:10, a = a), nl.grad(1:10, f, a = a), tolerance = tol) # Test nloptr:::finite.diff on multivariate Jacobian of vector function x0 <- 1:3 fn1 <- function(x) { c(3 * x[1L] ^ 2 * x[2L] * log(x[3L]), x[3] ^ 3 - 2 * x[1L] * x[2L]) } jac1 <- function(x) { matrix(c(6 * x[1L] * x[2L] * log(x[3L]), 3 * x[1L] ^ 2 * log(x[3L]), 3 * x[1L] ^ 2 * x[2L] / x[3L], -2 * x[2L], -2 * x[1L], 3 * x[3L] ^ 2), nrow = 2L, byrow = TRUE) } expect_equal(nloptr:::finite.diff(fn1, x0), jac1(x0), tolerance = tol) res <- suppressMessages( check.derivatives( .x = 1:10, func = f, func_grad = f_grad, check_derivatives_print = "none", a = a ) ) expect_identical(sum(res$flag_derivative_warning), 0L) # Define gradient function with 1 error. f_grad <- function(x, a) 2 * (x - a) + c(0, 0.1, rep(0, 8L)) res <- suppressMessages( check.derivatives( .x = 1:10, func = f, func_grad = f_grad, check_derivatives_print = "none", a = a ) ) expect_identical(sum(res$flag_derivative_warning), 1L) # Define objective function. g <- function(x, a) c(sum(x - a), sum((x - a) ^ 2)) # Define gradient function with 2 errors. g_grad <- function(x, a) { rbind(rep(1, length(x)) + c(0, 0.01, rep(0, 8L)), 2 * (x - a) + c(0, 0.1, rep(0, 8L))) } res <- suppressMessages( check.derivatives( .x = 1:10, func = g, func_grad = g_grad, check_derivatives_print = "none", a = a ) ) expect_identical(sum(res$flag_derivative_warning), 2L) nloptr/inst/tinytest/test-gradients.R0000644000176200001440000000326714472716401017526 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-gradients # Author: Avraham Adler # Date: 6 February 2023 # # Test code in nl.grad and nl.jacobian functions that is not tested elsewhere. # # Changelog: # library(nloptr) tol <- sqrt(.Machine$double.eps) fn1 <- function(x) sum(x ^ 2) fn2 <- function(x) c(3, 5) expect_error(nl.grad("C", fn1), "Argument 'x0' must be a numeric value.", fixed = TRUE) expect_error(nl.grad(2, fn2), "Function 'f' must be a scalar function (return a single value).", fixed = TRUE) expect_error(nl.jacobian("C", fn1), "Argument 'x' must be a non-empty numeric vector.", fixed = TRUE) expect_error(nl.jacobian(NULL, fn1), "Argument 'x' must be a non-empty numeric vector.", fixed = TRUE) # Test accuracy of multivariate gradient of scalar function x0 <- c(-2, 2, 2, -1, -1) fnE <- function(x) exp(x[1] * x[2] * x[3] * x[4] * x[5]) grE <- function(x) { c(x[2] * x[3] * x[4] * x[5], x[1] * x[3] * x[4] * x[5], x[1] * x[2] * x[4] * x[5], x[1] * x[2] * x[3] * x[5], x[1] * x[2] * x[3] * x[4]) * exp(prod(x)) } expect_equal(nl.grad(x0, fnE), grE(x0), tolerance = tol) # Test accuracy of multivariate Jacobian of vector function x0 <- 1:3 fn1 <- function(x) { c(3 * x[1L] ^ 2 * x[2L] * log(x[3L]), x[3] ^ 3 - 2 * x[1L] * x[2L]) } jac1 <- function(x) { matrix(c(6 * x[1L] * x[2L] * log(x[3L]), 3 * x[1L] ^ 2 * log(x[3L]), 3 * x[1L] ^ 2 * x[2L] / x[3L], -2 * x[2L], -2 * x[1L], 3 * x[3L] ^ 2), nrow = 2L, byrow = TRUE) } expect_equal(nl.jacobian(x0, fn1), jac1(x0), tolerance = tol) nloptr/inst/tinytest/test-wrapper-slsqp.R0000644000176200001440000001430614633255630020363 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-slsqp # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls for the Sequential Quadratic Programming algorithm. # # Changelog: # 2023-08-23: Change _output to _stdout # library(nloptr) tol <- sqrt(.Machine$double.eps) depMess <- paste("The old behavior for hin >= 0 has been deprecated. Please", "restate the inequality to be <=0. The ability to use the old", "behavior will be removed in a future release.") # Taken from example x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} hin.hs100 <- function(x) {c( 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - 11 * x[7]) } gr.hs100 <- function(x) { c( 2 * x[1] - 20, 10 * x[2] - 120, 4 * x[3] ^ 3, 6 * x[4] - 66, 60 * x[5] ^ 5, 14 * x[6] - 4 * x[7] - 10, 4 * x[7] ^ 3 - 4 * x[6] - 8) } hinjac.hs100 <- function(x) { matrix(c(4 * x[1], 12 * x[2] ^ 3, 1, 8 * x[4], 5, 0, 0, 7, 3, 20 * x[3], 1, -1, 0, 0, 23, 2 * x[2], 0, 0, 0, 12 * x[6], -8, 8 * x[1] - 3 * x[2], 2 * x[2] - 3 * x[1], 4 * x[3], 0, 0, 5, -11), nrow = 4, byrow = TRUE) } hin2.hs100 <- function(x) -hin.hs100(x) # Needed to test old behavior hinjac2.hs100 <- function(x) -hinjac.hs100(x) # Needed to test old behavior gr.hs100.computed <- function(x) nl.grad(x, fn.hs100) hinjac.hs100.computed <- function(x) nl.jacobian(x, hin.hs100) hinjac2.hs100.computed <- function(x) nl.jacobian(x, hin2.hs100) # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(slsqp(x0.hs100, fn = fn.hs100, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(slsqp(x0.hs100, fn = fn.hs100)) # No passed gradient or Inequality Jacobians slsqpTest <- slsqp(x0.hs100, fn.hs100, hin = hin.hs100, deprecatedBehavior = FALSE) slsqpControl <- nloptr(x0 = x0.hs100, eval_f = fn.hs100, eval_grad_f = gr.hs100.computed, eval_g_ineq = hin.hs100, eval_jac_g_ineq = hinjac.hs100.computed, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-6, maxeval = 1000L)) expect_identical(slsqpTest$par, slsqpControl$solution) expect_identical(slsqpTest$value, slsqpControl$objective) expect_identical(slsqpTest$iter, slsqpControl$iterations) expect_identical(slsqpTest$convergence, slsqpControl$status) expect_identical(slsqpTest$message, slsqpControl$message) # Passed gradient or Inequality Jacobians slsqpTest <- slsqp(x0.hs100, fn = fn.hs100, gr = gr.hs100, hin = hin.hs100, hinjac = hinjac.hs100, deprecatedBehavior = FALSE) # Going to be reused below in new behavior test. slsqpControlhinjac <- nloptr(x0 = x0.hs100, eval_f = fn.hs100, eval_grad_f = gr.hs100, eval_g_ineq = hin.hs100, eval_jac_g_ineq = hinjac.hs100, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-6, maxeval = 1000L)) expect_identical(slsqpTest$par, slsqpControlhinjac$solution) expect_identical(slsqpTest$value, slsqpControlhinjac$objective) expect_identical(slsqpTest$iter, slsqpControlhinjac$iterations) expect_identical(slsqpTest$convergence, slsqpControlhinjac$status) expect_identical(slsqpTest$message, slsqpControlhinjac$message) # Not passing equality Jacobian slsqpTest <- slsqp(x0.hs100, fn = fn.hs100, heq = hin.hs100, deprecatedBehavior = FALSE) slsqpControl <- nloptr(x0 = x0.hs100, eval_f = fn.hs100, eval_grad_f = gr.hs100.computed, eval_g_eq = hin.hs100, eval_jac_g_eq = hinjac.hs100.computed, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-6, maxeval = 1000L)) expect_equal(slsqpTest$par, slsqpControl$solution, tolerance = tol) expect_equal(slsqpTest$value, slsqpControl$objective, tolerance = tol) expect_identical(slsqpTest$iter, slsqpControl$iterations) expect_identical(slsqpTest$convergence, slsqpControl$status) expect_identical(slsqpTest$message, slsqpControl$message) # Passing equality Jacobian slsqpTest <- slsqp(x0.hs100, fn = fn.hs100, gr = gr.hs100, heq = hin.hs100, heqjac = hinjac.hs100, deprecatedBehavior = FALSE) slsqpControl <- nloptr(x0 = x0.hs100, eval_f = fn.hs100, eval_grad_f = gr.hs100, eval_g_eq = hin.hs100, eval_jac_g_eq = hinjac.hs100, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-6, maxeval = 1000L)) expect_identical(slsqpTest$par, slsqpControl$solution) expect_identical(slsqpTest$value, slsqpControl$objective) expect_identical(slsqpTest$iter, slsqpControl$iterations) expect_identical(slsqpTest$convergence, slsqpControl$status) expect_identical(slsqpTest$message, slsqpControl$message) # Test deprecated message expect_warning(slsqp(x0.hs100, fn = fn.hs100, hin = hin2.hs100), depMess) # Test deprecated behavior Adjust tests above when old behavior made defunct. slsqpTest <- suppressWarnings(slsqp(x0.hs100, fn = fn.hs100, gr = gr.hs100, hin = hin2.hs100, hinjac = hinjac2.hs100)) expect_identical(slsqpTest$par, slsqpControlhinjac$solution) expect_identical(slsqpTest$value, slsqpControlhinjac$objective) expect_identical(slsqpTest$iter, slsqpControlhinjac$iterations) expect_identical(slsqpTest$convergence, slsqpControlhinjac$status) expect_identical(slsqpTest$message, slsqpControlhinjac$message) nloptr/inst/tinytest/test-check.derivatives.R0000644000176200001440000000267214472716401021146 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-check.derivatives # Author: Avraham Adler # Date: 6 February 2023 # # Test code in "check.derivatives" function that is not tested elsewhere. # # Changelog: # library(nloptr) options(digits=7) f <- function(x, a) {sum((x - a) ^ 2)} f_grad <- function(x, a) {2 * (x - a)} expect_warning(suppressMessages(check.derivatives(.x = 1:10, func = f, func_grad = f_grad, check_derivatives_print = "z", a = runif(10L))), "for check_derivatives_print is unknown; use 'all'", fixed = TRUE) expect_message(check.derivatives(.x = 1:10, func = f, func_grad = f_grad, check_derivatives_print = "all", a = 1:10), "] = 0e+00 ~ 1.490116e-08 [", fixed = TRUE) expect_message(check.derivatives(.x = 1:10, func = f, func_grad = f_grad, check_derivatives_print = "all", a = 1:10), "Derivative checker results: 10 error(s) detected.", fixed = TRUE) expect_message(check.derivatives(.x = 1:10, func = f, func_grad = f_grad, check_derivatives_print = "errors", a = 1:10), "] = 0e+00 ~ 2.980232e-08 [1e+00]", fixed = TRUE) nloptr/inst/tinytest/test-wrapper-nm.R0000644000176200001440000000366614472716401017641 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-nm # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls for Nelder-Mead and Subplex algorithms. # # Changelog: # 2023-08-23: Change _output to _stdout # library(nloptr) ## Functions for the algorithms fphv <- function(x) { 100 * (x[3L] - 10 * atan2(x[2L], x[1L]) / (2 * pi)) ^ 2 + (sqrt(x[1L] ^ 2 + x[2L] ^ 2) - 1) ^ 2 + x[3L] ^ 2 } x0 <- c(-1, 0.5, 0.5) ## Nelder-Mead # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(neldermead(x0, fphv, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(neldermead(x0, fphv)) nmTest <- neldermead(x0, fphv) nmControl <- nloptr(x0 = x0, eval_f = fphv, opts = list(algorithm = "NLOPT_LN_NELDERMEAD", xtol_rel = 1e-6, maxeval = 1000L)) expect_identical(nmTest$par, nmControl$solution) expect_identical(nmTest$value, nmControl$objective) expect_identical(nmTest$iter, nmControl$iterations) expect_identical(nmTest$convergence, nmControl$status) expect_identical(nmTest$message, nmControl$message) ## Subplex # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(sbplx(x0, fphv, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(sbplx(x0, fphv)) sbplTest <- sbplx(x0, fphv) sbplControl <- nloptr(x0 = x0, eval_f = fphv, opts = list(algorithm = "NLOPT_LN_SBPLX", xtol_rel = 1e-6, maxeval = 1000L)) expect_identical(sbplTest$par, sbplControl$solution) expect_identical(sbplTest$value, sbplControl$objective) expect_identical(sbplTest$iter, sbplControl$iterations) expect_identical(sbplTest$convergence, sbplControl$status) expect_identical(sbplTest$message, sbplControl$message) nloptr/inst/tinytest/test-Rosenbrock-banana.R0000644000176200001440000002514214760162227021070 0ustar liggesusers# Copyright (C) 2024 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-Rosebbrock-banana # Author: Avraham Adler # Date: 25 June 2024 # # Complete rewrite of the current Rosenbrock banana tests. This also helps test # the accuracy of various algorithms. # # Changelog: # 2024-06-25: Complete rewrite of existing (inefficient) tests. Also tests # most of the exposed algorithms. See the comments here and # https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/ for # more details. # library(nloptr) tol <- sqrt(.Machine$double.eps) # Rosenbrock banana function (rbf) rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2} # Analytic gradient for rbf rbfgr <- function(x) {c(-2 * (1 - x[1]) - 400 * x[1] * (x[2] - x[1] ^ 2), 200 * (x[2] - x[1] ^ 2))} # Used options opts <- list(ftol_rel = 1e-12, xtol_rel = 1e-12, print_level = 0, maxeval = 5e4) # Known optimium of 0 occurs at (1, 1) rbfOptVal <- 0 rbfOptLoc <- c(1, 1) # Initial values x0 <- c(-1.2, 1.3) # Local Gradient-Based Algorithms ## LBFGS (also tests seperate and combined function/gradient calls). opts$algorithm <- "NLOPT_LD_LBFGS" # Test passing function and gradient separately. testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) # Test passing function and gradient in same function call. rbfComplete <- function(x) { list(objective = rbf(x), gradient = rbfgr(x)) } testRes <- nloptr(x0 = x0, eval_f = rbfComplete, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## MMA opts$algorithm <- "NLOPT_LD_MMA" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## CCSAQ opts$algorithm <- "NLOPT_LD_CCSAQ" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## SLSQP opts$algorithm <- "NLOPT_LD_SLSQP" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## Preconditioned truncated Newton opts$algorithm <- "NLOPT_LD_TNEWTON" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) opts$algorithm <- "NLOPT_LD_TNEWTON_RESTART" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) opts$algorithm <- "NLOPT_LD_TNEWTON_PRECOND" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) opts$algorithm <- "NLOPT_LD_TNEWTON_PRECOND_RESTART" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## Shifted limited-memory variable-metric opts$algorithm <- "NLOPT_LD_VAR2" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = 1e-7) opts$algorithm <- "NLOPT_LD_VAR1" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) # Local Derivative-Free Algorithms ## COBYLA opts$algorithm <- "NLOPT_LN_COBYLA" testRes <- nloptr(x0 = x0, eval_f = rbf, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## BOBYQA opts$algorithm <- "NLOPT_LN_BOBYQA" testRes <- nloptr(x0 = x0, eval_f = rbf, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## NEWUOA opts$algorithm <- "NLOPT_LN_NEWUOA" testRes <- nloptr(x0 = x0, eval_f = rbf, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## PRAXIS opts$algorithm <- "NLOPT_LN_PRAXIS" testRes <- nloptr(x0 = x0, eval_f = rbf, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## Nelder-Mead Simplex opts$algorithm <- "NLOPT_LN_NELDERMEAD" testRes <- nloptr(x0 = x0, eval_f = rbf, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## Sbplx opts$algorithm <- "NLOPT_LN_SBPLX" testRes <- nloptr(x0 = x0, eval_f = rbf, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) # Global Algorithms lb <- c(-3, -3) ub <- c(3, 3) ## StoGo ## StoGo passes on many platforms but fails MISERABLE (Inf???) on others. Note ## that here and disable the tests for now. # opts$algorithm <- "NLOPT_GD_STOGO" # testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, lb = lb, ub = ub, # opts = opts) # # expect_equal(testRes$objective, rbfOptVal, tolerance = 1e-4) # expect_equal(testRes$solution, rbfOptLoc, tolerance = 1e-4) # # opts$algorithm <- "NLOPT_GD_STOGO_RAND" # testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, lb = lb, ub = ub, # opts = opts) # # expect_equal(testRes$objective, rbfOptVal, tolerance = 1e-4) # expect_equal(testRes$solution, rbfOptLoc, tolerance = 1e-4) ## ISRES opts$population <- 100 opts$ranseed <- 2718L opts$algorithm <- "NLOPT_GN_ISRES" testRes <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) ## Controlled Random Search (with ranseed testing) opts$algorithm <- "NLOPT_GN_CRS2_LM" testRes <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) # Different random seed opts$ranseed <- 3141L testRes2 <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) # Same random seed opts$ranseed <- 2718L testRes3 <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) # Results of different random seeds should differ. expect_false(identical(testRes$objective, testRes2$objective)) expect_false(identical(testRes$solution, testRes2$solution)) # Results of same random seeds should be the same. expect_identical(testRes$objective, testRes3$objective) expect_identical(testRes$solution, testRes3$solution) ## DIRECT opts$algorithm <- "NLOPT_GN_DIRECT_L" testRes <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) # expect_equal(testRes$objective, rbfOptVal, tolerance = tol) # expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) opts$algorithm <- "NLOPT_GN_DIRECT_NOSCAL" testRes <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) opts$algorithm <- "NLOPT_GN_DIRECT_L_NOSCAL" testRes <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) opts$algorithm <- "NLOPT_GN_DIRECT_L_RAND_NOSCAL" testRes <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) opts$algorithm <- "NLOPT_GN_ORIG_DIRECT_L" testRes <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) # The follwing versions converge to the wrong answer; see # https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#direct-and-direct-l # in that the rescaling may be faulty for this particular problem. opts$algorithm <- "NLOPT_GN_DIRECT" expect_stdout(nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts)) opts$algorithm <- "NLOPT_GN_ORIG_DIRECT" expect_stdout(nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts)) ## ESCH - does not converge in 1M iterations so just test for output. Probably ## needs MUCH tighter bounds. opts$algorithm <- "NLOPT_GN_ESCH" expect_stdout(nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts)) ## MLSL (Multi-Level Single-Linkage) # Use LBGFS as local search algorithm opts$local_opts <- list(algorithm = "NLOPT_LD_LBFGS", xtol_rel = 1e-9) # Need to set lower evaluation cap since this is nested global/local oldmaxeval <- opts$maxeval opts$maxeval <- 1000 # Gradient-based opts$algorithm <- "NLOPT_GD_MLSL" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) opts$algorithm <- "NLOPT_GD_MLSL_LDS" testRes <- nloptr(x0 = x0, eval_f = rbf, eval_grad_f = rbfgr, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = tol) expect_equal(testRes$solution, rbfOptLoc, tolerance = tol) # Derivative-free opts$local_opts <- list(algorithm = "NLOPT_LN_NELDERMEAD", xtol_rel = 1e-12) opts$maxeval <- 10000 # Need lower tolerance (or MANY more evaluations) without gradient information. opts$algorithm <- "NLOPT_GN_MLSL" testRes <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = 1e-5) expect_equal(testRes$solution, rbfOptLoc, tolerance = 1e-5) opts$algorithm <- "NLOPT_GN_MLSL_LDS" testRes <- nloptr(x0 = x0, eval_f = rbf, lb = lb, ub = ub, opts = opts) expect_equal(testRes$objective, rbfOptVal, tolerance = 1e-5) expect_equal(testRes$solution, rbfOptLoc, tolerance = 1e-5) nloptr/inst/tinytest/test-is.nloptr.R0000644000176200001440000002215614472716401017474 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-is.nloptr # Author: Avraham Adler # Date: 6 February 2023 # # Test code in "is.nloptr" function that is not tested elsewhere. # # Changelog: # library(nloptr) ctlNM <- list(algorithm = "NLOPT_LN_NELDERMEAD", xtol_rel = 1e-8) ctlLB <- list(algorithm = "NLOPT_LD_LBFGS", xtol_rel = 1e-8) # Check whether the object exists and is a list expect_false(is.nloptr(NULL)) expect_false(is.nloptr(3)) # Check whether the needed wrapper functions are supplied # This seems to ALWAYS be preempted by .checkfunargs in nloptr itself (AA) fphv <- function(x) { 100 * (x[3L] - 10 * atan2(x[2L], x[1L]) / (2 * pi)) ^ 2 + (sqrt(x[1L] ^ 2 + x[2L] ^ 2) - 1) ^ 2 + x[3L] ^ 2 } # Check whether bounds are defined for all controls expect_error(nloptr(x0 = c(-1.2, 1.5, NA), eval_f = fphv, opts = ctlNM), "x0 contains NA", fixed = TRUE) expect_error(nloptr(x0 = c(-1.2, 1.5, 3), eval_f = fphv, lb = c(-2, -2), opts = ctlNM), "length(lb) != length(x0)", fixed = TRUE) expect_error(nloptr(x0 = c(-1.2, 1.5, 3), eval_f = fphv, ub = c(-2, -2), opts = ctlNM), "length(ub) != length(x0)", fixed = TRUE) # Check whether the initial value is within the bounds expect_error(nloptr(x0 = c(-1.2, 1.5, 3), eval_f = fphv, lb = c(-1, -1, -1), opts = ctlNM), "at least one element in x0 < lb", fixed = TRUE) expect_error(nloptr(x0 = c(-1.2, 1.5, 3), eval_f = fphv, ub = c(2, 2, 2), opts = ctlNM), "at least one element in x0 > ub", fixed = TRUE) # check if an existing algorithm was supplied expect_error(nloptr(x0 = c(-1.2, 1.5, 3), eval_f = fphv, opts = list(algorithm = "NLOPT_LN_NEDERMEAD", xtol_rel = 1e-8)), "Incorrect algorithm supplied. Use one of the", fixed = TRUE) # Check that we don't have NA's if we evaluate the objective function in x0. f0 <- function(x) 3 * x ^ 1.5 - 2 * x ^ 0.5 expect_error(suppressWarnings(nloptr(x0 = -1, eval_f = f0, opts = ctlNM)), "objective in x0 returns NA", fixed = TRUE) f0 <- function(x) 3 * x ^ 4 - 12 * x ^ 3 g0 <- function(x) 4 * sqrt(x) # Yes it's not the gradient. This is a unit test!! expect_error(suppressWarnings(nloptr(x0 = -1, f0, g0, opts = ctlLB)), "objective in x0 returns NA", fixed = TRUE) g0 <- function(x) c(4, 2) # Yes it's not the gradient. This is a unit test!! expect_error(suppressWarnings(nloptr(x0 = -1, f0, g0, opts = ctlLB)), "wrong number of elements in gradient of objective", fixed = TRUE) # check whether algorithm needs a derivative g0 <- function(x) 12 * x ^ 3 - 36 * x ^ 2 # Actual gradient ## Just checking... expect_silent(nloptr(x0 = -1, f0, g0, opts = ctlLB)) expect_warning(nloptr(x0 = -1, f0, g0, opts = ctlNM), "a gradient was supplied for the objective function", fixed = TRUE) expect_error(nloptr(x0 = -1, f0, opts = ctlLB), "A gradient for the objective function is needed", fixed = TRUE) # Malformed objects solely intended to trigger tests: ## eval_f test expect_error(is.nloptr(list(eval_f = "Hello")), "eval_f is not a function") ## eval_g_ineq test expect_error(is.nloptr(list(eval_f = fphv, eval_g_ineq = "GoodBye")), "eval_g_ineq is not a function") ## eval_g_eq test expect_error(is.nloptr(list(eval_f = fphv, eval_g_eq = 27)), "eval_g_eq is not a function") ## MULTIVARIATE FUNCTION WITH CONSTRAINTS x0 <- c(2, 2) ub <- c(5, 5) lb <- c(-1, -1) fn <- function(x) (x[1L] - 1) ^ 2 + (x[2L] - 1) ^ 2 + 1 gr <- function(x) c(2 * (x[1L] - 1), 2 * (x[2L] - 1)) fnl <- function(x) list("objective" = fn(x), "gradient" = gr(x)) fnlNA <- function(x) list("objective" = NA_real_, "gradient" = gr(x)) hin <- function(x) c(1.44 - x[1L] ^ 2, 2.197 - x[2L] ^ 3) hinjac <- function(x) matrix(c(-2 * x[1L], 0, 0, -3 * x[2L] ^ 2), 2L, 2L) hinl <- function(x) list("constraints" = hin(x), "jacobian" = hinjac(x)) hinlNA <- function(x) { list("constraints" = hin(NA_real_), "jacobian" = hinjac(x)) } heq <- function(x) c(x[1L] * x[2L] - 2.55, x[1L] - x[2L] - 0.2) heqjac <- function(x) matrix(c(x[2L], 1, x[1L], -1), 2L) heql <- function(x) list("constraints" = heq(x), "jacobian" = heqjac(x)) heqlNA <- function(x) { list("constraints" = heq(NA_real_), "jacobian" = heqjac(x)) } optSol <- c(1.7, 1.5) optVal <- 1.74 # Test simple error messages first; roughly in their order in is.nloptr.R Many # of these are testing the list versions of their functional parents. A list # version is when a function and its gradient are returned in the same call. expect_error(nloptr(x0, fnlNA, opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-8)), "objective in x0 returns NA", fixed = TRUE) hinE <- function(x) c(4, NA_real_) expect_error(nloptr(x0, fn, eval_g_ineq = hinE, opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-8)), "inequality constraints in x0 returns NA", fixed = TRUE) expect_error(nloptr(x0, fnl, eval_g_ineq = hinlNA, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8)), "inequality constraints in x0 returns NA", fixed = TRUE) hinjacE <- function(x) c(-2 * x[1L], NA_real_) expect_error(nloptr(x0, fn, gr, eval_g_ineq = hin, eval_jac_g_ineq = hinjacE, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8)), "jacobian of inequality constraints in x0 returns NA", fixed = TRUE) hinjacE <- function(x) c(-2 * x[1L], -3 * x[2L] ^ 2) expect_error(nloptr(x0, fn, gr, eval_g_ineq = hin, eval_jac_g_ineq = hinjacE, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8)), "wrong number of elements in jacobian of inequality", fixed = TRUE) expect_warning(nloptr(x0, fn, eval_g_ineq = hin, eval_jac_g_ineq = hinjac, opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-8)), "gradient was supplied for the inequality constraints", fixed = TRUE) expect_error(nloptr(x0, fn, gr, eval_g_ineq = hin, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8)), "gradient for the inequality constraints is needed", fixed = TRUE) heqE <- function(x) c(x[1L] * x[2L] - 2.55, NA_real_) expect_error(nloptr(x0, fn, eval_g_eq = heqE, opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-8)), "equality constraints in x0 returns NA", fixed = TRUE) expect_error(nloptr(x0, fn, eval_g_eq = heqlNA, opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-8)), "equality constraints in x0 returns NA", fixed = TRUE) heqjacE <- function(x) c(-2 * x[1L], NA_real_) expect_error(nloptr(x0, fn, gr, eval_g_eq = heq, eval_jac_g_eq = heqjacE, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8)), "jacobian of equality constraints in x0 returns NA", fixed = TRUE) heqjacE <- function(x) c(-2 * x[1L], -3 * x[2L] ^ 2) expect_error(nloptr(x0, fn, gr, eval_g_eq = heq, eval_jac_g_eq = heqjacE, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8)), "wrong number of elements in jacobian of equality", fixed = TRUE) expect_warning(nloptr(x0, fn, eval_g_eq = heq, eval_jac_g_eq = heqjac, opts = list(algorithm = "NLOPT_GN_ISRES", xtol_rel = 1e-8)), "gradient was supplied for the equality constraints", fixed = TRUE) expect_error(nloptr(x0, fn, gr, eval_g_eq = heq, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8)), "gradient for the equality constraints is needed", fixed = TRUE) expect_error(nloptr(x0, fn, gr, eval_g_eq = heq, eval_jac_g_eq = heqjac, opts = list(algorithm = "NLOPT_LD_LBFGS", xtol_rel = 1e-8)), "If you want to use equality constraints, then you should use one", fixed = TRUE) expect_error(nloptr(x0, fn, gr, eval_g_eq = heq, eval_jac_g_eq = heqjac, opts = list(algorithm = "NLOPT_LD_AUGLAG", xtol_rel = 1e-8)), "needs a local optimizer; specify an algorithm and termination", fixed = TRUE) expect_error(nloptr(x0, fn, gr, eval_g_ineq = hin, eval_jac_g_ineq = hinjac, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8, tol_constraints_ineq = rep(0.1, 3L))), "The vector tol_constraints_ineq in the options list", fixed = TRUE) expect_error(nloptr(x0, fn, gr, eval_g_eq = heq, eval_jac_g_eq = heqjac, opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-8, tol_constraints_eq = rep(0.1, 3L))), "The vector tol_constraints_eq in the options list", fixed = TRUE) nloptr/inst/tinytest/test-nloptr.print.options.R0000644000176200001440000000160614472716401021704 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-nloptr.print.options # Author: Avraham Adler # Date: 7 February 2023 # # Test code in "nloptr.print.options" function that is not tested elsewhere. # # Changelog: # 2023-08-23: tinytest has no "snapshot" equivalent so removed that test. # Converted the others to tinytest format. # library(nloptr) expect_stdout(nloptr.print.options(opts.show = "check_derivatives"), "user-supplied analytic gradients with finite difference", fixed = TRUE) expect_stdout(nloptr(3, function(x) x ^ 2 + 1, opts = list(algorithm = "NLOPT_LN_NELDERMEAD", xtol_rel = 1e-8, print_options_doc = TRUE)), "user-supplied analytic gradients with finite difference", fixed = TRUE) nloptr/inst/tinytest/test-wrapper-tnewton.R0000644000176200001440000001043614472716401020716 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-tnewton # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls to Preconditioned Truncated Newton algorithms. # # Changelog: # 2023-08-23: Change _output to _stdout # library(nloptr) ## Functions for the algorithms flb <- function(x) { p <- length(x) sum(c(1, rep(4, p - 1)) * (x - c(1, x[-p]) ^ 2) ^ 2) } x0 <- rep(3, 25L) lb <- rep(2, 25L) ub <- rep(4, 25L) ctl <- list(xtol_rel = 1e-8) # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(tnewton(x0, flb, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(tnewton(x0, flb)) # No passed gradient; Restart; Precond tnTest <- tnewton(x0, flb, lower = lb, upper = ub, control = ctl) tnControl <- nloptr(x0 = x0, eval_f = flb, eval_grad_f = function(x) nl.grad(x, flb), lb = lb, ub = ub, opts = list(algorithm = "NLOPT_LD_TNEWTON_PRECOND_RESTART", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(tnTest$par, tnControl$solution) expect_identical(tnTest$value, tnControl$objective) expect_identical(tnTest$iter, tnControl$iterations) expect_identical(tnTest$convergence, tnControl$status) expect_identical(tnTest$message, tnControl$message) # No passed gradient: Restart; No Precond tnTest <- tnewton(x0, flb, lower = lb, upper = ub, control = ctl, precond = FALSE) tnControl <- nloptr(x0 = x0, eval_f = flb, eval_grad_f = function(x) nl.grad(x, flb), lb = lb, ub = ub, opts = list(algorithm = "NLOPT_LD_TNEWTON_RESTART", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(tnTest$par, tnControl$solution) expect_identical(tnTest$value, tnControl$objective) expect_identical(tnTest$iter, tnControl$iterations) expect_identical(tnTest$convergence, tnControl$status) expect_identical(tnTest$message, tnControl$message) # No passed gradient: No Restart; Precond tnTest <- tnewton(x0, flb, lower = lb, upper = ub, control = ctl, restart = FALSE) tnControl <- nloptr(x0 = x0, eval_f = flb, eval_grad_f = function(x) nl.grad(x, flb), lb = lb, ub = ub, opts = list(algorithm = "NLOPT_LD_TNEWTON_PRECOND", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(tnTest$par, tnControl$solution) expect_identical(tnTest$value, tnControl$objective) expect_identical(tnTest$iter, tnControl$iterations) expect_identical(tnTest$convergence, tnControl$status) expect_identical(tnTest$message, tnControl$message) # No passed gradient: No Restart; No Precond tnTest <- tnewton(x0, flb, lower = lb, upper = ub, control = ctl, restart = FALSE, precond = FALSE) tnControl <- nloptr(x0 = x0, eval_f = flb, eval_grad_f = function(x) nl.grad(x, flb), lb = lb, ub = ub, opts = list(algorithm = "NLOPT_LD_TNEWTON", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(tnTest$par, tnControl$solution) expect_identical(tnTest$value, tnControl$objective) expect_identical(tnTest$iter, tnControl$iterations) expect_identical(tnTest$convergence, tnControl$status) expect_identical(tnTest$message, tnControl$message) # Passed gradient fr <- function(x) {100 * (x[2L] - x[1L] ^ 2) ^ 2 + (1 - x[1L]) ^ 2} gr <- function(x) { .expr2 <- x[2L] - x[1L] ^ 2 .expr5 <- 1 - x[1L] c(-(2 * .expr5 + 100 * (2 * (2 * x[1L] * .expr2))), 100 * (2 * .expr2)) } tnTest <- tnewton(c(-1.2, 2), fr, gr, control = ctl) tnControl <- nloptr(x0 = c(-1.2, 2), eval_f = fr, eval_grad_f = gr, opts = list(algorithm = "NLOPT_LD_TNEWTON_PRECOND_RESTART", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(tnTest$par, tnControl$solution) expect_identical(tnTest$value, tnControl$objective) expect_identical(tnTest$iter, tnControl$iterations) expect_identical(tnTest$convergence, tnControl$status) expect_identical(tnTest$message, tnControl$message) nloptr/inst/tinytest/test-simple.R0000644000176200001440000000467714472716401017045 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-simple.R # Author: Jelmer Ypma # Date: 20 June 2010 # # Maintenance assumed by Avraham Adler (AA) on 2023-02-10 # # Example showing how to solve a simple constrained problem. # # min x^2 # s.t. x >= 5 # # re-formulate constraint to be of form g(x) <= 0 # 5 - x <= 0 # we could use a bound constraint as well here # # CHANGELOG: # 2014-05-05: Changed example to use unit testing framework testthat. # 2019-12-12: Corrected warnings and using updated testtthat framework (AA) # 2023-02-07: Remove wrapping tests in "test_that" to reduce duplication. (AA) # library(nloptr) tol <- sqrt(.Machine$double.eps) # Test simple constrained optimization problem with gradient information. # Objective function eval_f <- function(x) x ^ 2 # Gradient of objective function. eval_grad_f <- function(x) 2 * x # Inequality constraint function. eval_g_ineq <- function(x) 5 - x # Jacobian of constraint. eval_jac_g_ineq <- function(x) -1 # Optimal solution. solution.opt <- 5 # Solve using NLOPT_LD_MMA with gradient information supplied in separate # function. res <- nloptr(x0 = 1, eval_f = eval_f, eval_grad_f = eval_grad_f, eval_g_ineq = eval_g_ineq, eval_jac_g_ineq = eval_jac_g_ineq, opts = list("algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1e-4)) # Run some checks on the optimal solution. expect_equal(res$solution, solution.opt, tolerance = tol) # Check whether constraints are violated (up to specified tolerance). expect_true(eval_g_ineq(res$solution) <= res$options$tol_constraints_ineq) # Test simple constrained optimization problem without gradient information. # Solve using NLOPT_LN_COBYLA without gradient information res <- nloptr(x0 = 1, eval_f = eval_f, eval_g_ineq = eval_g_ineq, opts = list("algorithm" = "NLOPT_LN_COBYLA", "xtol_rel" = 1e-6, "tol_constraints_ineq" = 1e-6)) # Run some checks on the optimal solution. expect_equal(res$solution, solution.opt, tolerance = 1e-6) # Check whether constraints are violated (up to specified tolerance). expect_true(eval_g_ineq(res$solution) <= res$options$tol_constraints_ineq) nloptr/inst/tinytest/test-wrapper-mlsl.R0000644000176200001440000000672314472716401020173 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-mlsl # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls MLSL algorithm. # # Changelog: # 2023-08-23: Change _stdout to _stdout and _lte to _true # library(nloptr) tol <- 8e-8 ## Functions for the algorithms hartmann6 <- function(x) { a <- c(1, 1.2, 3, 3.2) A <- matrix(c(10, 0.05, 3, 17, 3, 10, 3.5, 8, 17, 17, 1.7, 0.05, 3.5, 0.1, 10, 10, 1.7, 8, 17, 0.1, 8, 14, 8, 14), nrow = 4L, ncol = 6L) B <- matrix(c(0.1312, 0.2329, 0.2348, 0.4047, 0.1696, 0.4135, 0.1451, 0.8828, 0.5569, 0.8307, 0.3522, 0.8732, 0.0124, 0.3736, 0.2883, 0.5743, 0.8283, 0.1004, 0.3047, 0.1091, 0.5886, 0.9991, 0.6650, 0.0381), nrow = 4L, ncol = 6L) fun <- 0 for (i in 1:4) { fun <- fun - a[i] * exp(-sum(A[i, ] * (x - B[i, ]) ^ 2)) } fun } hart.gr <- function(x) nl.grad(x, hartmann6) x0 <- lb <- rep(0, 6L) ub <- rep(1, 6L) ctl <- list(xtol_rel = 1e-8, maxeval = 750L) lopt <- list(algorithm = "NLOPT_LD_LBFGS", xtol_rel = 1e-4) # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(mlsl(x0 = x0, hartmann6, lower = lb, upper = ub, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(mlsl(x0 = x0, hartmann6, lower = lb, upper = ub)) # Test Warning expect_warning(mlsl(x0, hartmann6, hart.gr, lb, ub, local.method = "MMA"), "Only gradient-based LBFGS available as local met", fixed = TRUE) # No passed gradient: Low discrepancy mlslTest <- mlsl(x0, hartmann6, lower = lb, upper = ub, control = ctl) mlslControl <- nloptr(x0 = x0, eval_f = hartmann6, eval_grad_f = hart.gr, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GD_MLSL_LDS", xtol_rel = 1e-8, maxeval = 750L, local_opts = lopt)) expect_identical(mlslTest$par, mlslControl$solution) expect_identical(mlslTest$value, mlslControl$objective) expect_identical(mlslTest$iter, mlslControl$iterations) expect_identical(mlslTest$convergence, mlslControl$status) expect_identical(mlslTest$message, mlslControl$message) # Passed gradient: No low discrepancy mlslTest <- mlsl(x0, hartmann6, hart.gr, lb, ub, low.discrepancy = FALSE, control = ctl) mlslControl <- nloptr(x0 = x0, eval_f = hartmann6, eval_grad_f = hart.gr, lb = lb, ub = ub, opts = list(algorithm = "NLOPT_GD_MLSL", xtol_rel = 1e-8, maxeval = 750L, local_opts = lopt)) expect_equal(mlslTest$par, mlslControl$solution, tolerance = tol) expect_equal(mlslTest$value, mlslControl$objective, tolerance = tol) # See https://nlopt.readthedocs.io/en/latest/NLopt_Reference/#stopping-criteria # "This is not a strict maximum: the number of function evaluations may exceed # maxeval slightly, depending upon the algorithm." expect_true(abs(mlslTest$iter - mlslControl$iterations) <= 10L) expect_identical(mlslTest$convergence, mlslControl$status) expect_identical(mlslTest$message, mlslControl$message) nloptr/inst/tinytest/test-wrapper-ccsaq.R0000644000176200001440000001226614633255630020316 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-ccsaq # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls to ccsaq algorithm # # Changelog: # 2023-08-23: Change _output to _stdout # library(nloptr) depMess <- paste("The old behavior for hin >= 0 has been deprecated. Please", "restate the inequality to be <=0. The ability to use the old", "behavior will be removed in a future release.") # Taken from example x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} hin.hs100 <- function(x) {c( 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - 11 * x[7]) } gr.hs100 <- function(x) { c( 2 * x[1] - 20, 10 * x[2] - 120, 4 * x[3] ^ 3, 6 * x[4] - 66, 60 * x[5] ^ 5, 14 * x[6] - 4 * x[7] - 10, 4 * x[7] ^ 3 - 4 * x[6] - 8) } hinjac.hs100 <- function(x) { matrix(c(4 * x[1], 12 * x[2] ^ 3, 1, 8 * x[4], 5, 0, 0, 7, 3, 20 * x[3], 1, -1, 0, 0, 23, 2 * x[2], 0, 0, 0, 12 * x[6], -8, 8 * x[1] - 3 * x[2], 2 * x[2] - 3 * x[1], 4 * x[3], 0, 0, 5, -11), nrow = 4, byrow = TRUE) } # In older version, the HS100 was not properly copied, so the gradients caused # an issue. This has since been corrected, but leaving the calls in to test the # gradient/Jacobian creation routines. gr.hs100.computed <- function(x) nl.grad(x, fn.hs100) hin2.hs100 <- function(x) -hin.hs100(x) # Needed to test old behavior hinjac2.hs100 <- function(x) -hinjac.hs100(x) # Needed to test old behavior hinjac.hs100.computed <- function(x) nl.jacobian(x, hin.hs100) # See example hinjac2.hs100.computed <- function(x) nl.jacobian(x, hin2.hs100) # See example ctl <- list(xtol_rel = 1e-8, maxeval = 1000L) # Test normal silent running expect_silent(ccsaq(x0.hs100, fn.hs100)) # Provides incorrect answer expect_silent(ccsaq(x0.hs100, fn.hs100, hin = hin.hs100, hinjac = hinjac.hs100, deprecatedBehavior = FALSE)) # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(ccsaq(x0.hs100, fn.hs100, nl.info = TRUE, deprecatedBehavior = FALSE), "Call:", fixed = TRUE) # Control for CCSAQ HS100 ## Exact ccsaqControlE <- nloptr( x0 = x0.hs100, eval_f = fn.hs100, eval_grad_f = gr.hs100, eval_g_ineq = hin.hs100, eval_jac_g_ineq = hinjac.hs100, opts = list(algorithm = "NLOPT_LD_CCSAQ", xtol_rel = 1e-8, maxeval = 1000L) ) ## Computed ccsaqControlC <- nloptr( x0 = x0.hs100, eval_f = fn.hs100, eval_grad_f = gr.hs100.computed, eval_g_ineq = hin.hs100, eval_jac_g_ineq = hinjac.hs100.computed, opts = list(algorithm = "NLOPT_LD_CCSAQ", xtol_rel = 1e-8, maxeval = 1000L) ) # Test no passed gradient or Jacobian (so algorithm computes). ccsaqTest <- ccsaq(x0.hs100, fn.hs100, hin = hin.hs100, control = ctl, deprecatedBehavior = FALSE) expect_identical(ccsaqTest$par, ccsaqControlC$solution) expect_identical(ccsaqTest$value, ccsaqControlC$objective) expect_identical(ccsaqTest$iter, ccsaqControlC$iterations) expect_identical(ccsaqTest$convergence, ccsaqControlC$status) expect_identical(ccsaqTest$message, ccsaqControlC$message) # Test passed gradient and Jacobian ## Exact ccsaqTest <- ccsaq(x0.hs100, fn.hs100, gr = gr.hs100, hin = hin.hs100, hinjac = hinjac.hs100, control = ctl, deprecatedBehavior = FALSE) expect_identical(ccsaqTest$par, ccsaqControlE$solution) expect_identical(ccsaqTest$value, ccsaqControlE$objective) expect_identical(ccsaqTest$iter, ccsaqControlE$iterations) expect_identical(ccsaqTest$convergence, ccsaqControlE$status) expect_identical(ccsaqTest$message, ccsaqControlE$message) ## Computed ccsaqTest <- ccsaq(x0.hs100, fn.hs100, gr = gr.hs100.computed, hin = hin.hs100, hinjac = hinjac.hs100.computed, control = ctl, deprecatedBehavior = FALSE) expect_identical(ccsaqTest$par, ccsaqControlC$solution) expect_identical(ccsaqTest$value, ccsaqControlC$objective) expect_identical(ccsaqTest$iter, ccsaqControlC$iterations) expect_identical(ccsaqTest$convergence, ccsaqControlC$status) expect_identical(ccsaqTest$message, ccsaqControlC$message) # Test deprecated behavior message expect_warning(ccsaq(x0.hs100, fn.hs100, hin = hin2.hs100), depMess) # Test deprecated behavior ccsaqTest <- suppressWarnings(ccsaq(x0.hs100, fn.hs100, gr = gr.hs100, hin = hin2.hs100, hinjac = hinjac2.hs100, control = ctl)) expect_identical(ccsaqTest$par, ccsaqControlE$solution) expect_identical(ccsaqTest$value, ccsaqControlE$objective) expect_identical(ccsaqTest$iter, ccsaqControlE$iterations) expect_identical(ccsaqTest$convergence, ccsaqControlE$status) expect_identical(ccsaqTest$message, ccsaqControlE$message) nloptr/inst/tinytest/test-hs071.R0000644000176200001440000000564414472716401016411 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-hs071.R # Author: Jelmer Ypma # Date: 10 June 2010 # # Maintenance assumed by Avraham Adler (AA) on 2023-02-10 # # Example problem, number 71 from the Hock-Schittkowsky test suite. # # \min_{x} x1*x4*(x1 + x2 + x3) + x3 # s.t. # x1*x2*x3*x4 >= 25 # x1^2 + x2^2 + x3^2 + x4^2 = 40 # 1 <= x1,x2,x3,x4 <= 5 # # we re-write the inequality as # 25 - x1*x2*x3*x4 <= 0 # # and the equality as # x1^2 + x2^2 + x3^2 + x4^2 - 40 = 0 # # x0 = (1,5,5,1) # # Optimal solution = (1.00000000, 4.74299963, 3.82114998, 1.37940829) # # CHANGELOG: # 2014-05-05: Changed example to use unit testing framework testthat. # 2019-12-12: Corrected warnings and using updated testtthat framework (AA) # 2023-02-07: Remove wrapping tests in "test_that" to reduce duplication. (AA) # library(nloptr) # f(x) = x1*x4*(x1 + x2 + x3) + x3 eval_f <- function(x) { list("objective" = x[1] * x[4] * (x[1] + x[2] + x[3]) + x[3], "gradient" = c(x[1] * x[4] + x[4] * (x[1] + x[2] + x[3]), x[1] * x[4], x[1] * x[4] + 1, x[1] * (x[1] + x[2] + x[3]))) } # Inequality constraints. eval_g_ineq <- function(x) { constr <- c(25 - x[1] * x[2] * x[3] * x[4]) grad <- c(-x[2] * x[3] * x[4], -x[1] * x[3] * x[4], -x[1] * x[2] * x[4], -x[1] * x[2] * x[3]) list("constraints" = constr, "jacobian" = grad) } # Equality constraints. eval_g_eq <- function(x) { constr <- c(x[1] ^ 2 + x[2] ^ 2 + x[3] ^ 2 + x[4] ^ 2 - 40) grad <- c(2.0 * x[1], 2.0 * x[2], 2.0 * x[3], 2.0 * x[4]) list("constraints" = constr, "jacobian" = grad) } # Initial values. x0 <- c(1, 5, 5, 1) # Lower and upper bounds of control. lb <- c(1, 1, 1, 1) ub <- c(5, 5, 5, 5) # Optimal solution. solution.opt <- c(1.00000000, 4.74299963, 3.82114998, 1.37940829) # Set optimization options. local_opts <- list("algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1.0e-7) opts <- list("algorithm" = "NLOPT_LD_AUGLAG", "xtol_rel" = 1.0e-7, "maxeval" = 1000, "local_opts" = local_opts, "print_level" = 0) # Do optimization. res <- nloptr(x0 = x0, eval_f = eval_f, lb = lb, ub = ub, eval_g_ineq = eval_g_ineq, eval_g_eq = eval_g_eq, opts = opts) # Run some checks on the optimal solution. expect_equal(res$solution, solution.opt, tolerance = 1e-5) expect_true(all(res$solution >= lb)) expect_true(all(res$solution <= ub)) # Check whether constraints are violated (up to specified tolerance). expect_true( eval_g_ineq(res$solution)$constr <= res$options$tol_constraints_ineq ) expect_equal(eval_g_eq(res$solution)$constr, 0, tolerance = res$options$tol_constraints_eq) nloptr/inst/tinytest/test-nloptr.add.default.options.R0000644000176200001440000000101614472716401022716 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-nloptr.add.default.options # Author: Avraham Adler # Date: 8 February 2023 # # Test code in nloptr.add.default.options function that is not tested elsewhere. # # Changelog: # library(nloptr) fn <- function(x) x ^ 2 - 4 * x + 4 expect_warning(nloptr(3, fn, opts = list(algorithm = "NLOPT_LN_NELDERMEAD")), "No termination criterion specified, using default", fixed = TRUE) nloptr/inst/tinytest/test-wrapper-cobyla.R0000644000176200001440000001064314633255630020472 0ustar liggesusers# Copyright (C) 2023 Avraham Adler. All Rights Reserved. # SPDX-License-Identifier: LGPL-3.0-or-later # # File: test-wrapper-cobyla # Author: Avraham Adler # Date: 6 February 2023 # # Test wrapper calls to cobyla, bobyqa, and newuoa algorithms # # CHANGELOG # # 2023-08-23: Change _output to _stdout # 2024-06-04: Switched desired direction of the hin/hinjac inequalities, leaving # the old behavior as the default for now. Also cleaned up the HS100 # example (Avraham Adler). # library(nloptr) depMess <- paste("The old behavior for hin >= 0 has been deprecated. Please", "restate the inequality to be <=0. The ability to use the old", "behavior will be removed in a future release.") ## Functions for COBYLA, BOBYQA, and NEWUOA x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} hin.hs100 <- function(x) {c( 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - 11 * x[7]) } hin2.hs100 <- function(x) -hin.hs100(x) # Needed to test old behavior rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2} ctl <- list(xtol_rel = 1e-8) # Test printout if nl.info passed. The word "Call:" should be in output if # passed and not if not passed. expect_stdout(cobyla(x0.hs100, fn.hs100, nl.info = TRUE, deprecatedBehavior = FALSE), "Call:", fixed = TRUE) expect_stdout(bobyqa(x0.hs100, fn.hs100, nl.info = TRUE), "Call:", fixed = TRUE) expect_stdout(newuoa(x0.hs100, fn.hs100, nl.info = TRUE), "Call:", fixed = TRUE) expect_silent(cobyla(x0.hs100, fn.hs100, deprecatedBehavior = FALSE)) expect_silent(bobyqa(x0.hs100, fn.hs100)) expect_silent(newuoa(x0.hs100, fn.hs100)) # Test COBYLA algorithm cobylaTest <- cobyla(x0.hs100, fn.hs100, hin = hin.hs100, control = ctl, deprecatedBehavior = FALSE) cobylaControl <- nloptr(x0 = x0.hs100, eval_f = fn.hs100, eval_g_ineq = hin.hs100, opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-8, maxeval = 1000L)) expect_identical(cobylaTest$par, cobylaControl$solution) expect_identical(cobylaTest$value, cobylaControl$objective) expect_identical(cobylaTest$iter, cobylaControl$iterations) expect_identical(cobylaTest$convergence, cobylaControl$status) expect_identical(cobylaTest$message, cobylaControl$message) # Test deprecated message expect_warning(cobyla(x0.hs100, fn.hs100, hin = hin2.hs100), depMess) # Test deprecated behavior cobylaTest <- suppressWarnings(cobyla(x0.hs100, fn.hs100, hin = hin2.hs100, control = ctl)) expect_identical(cobylaTest$par, cobylaControl$solution) expect_identical(cobylaTest$value, cobylaControl$objective) expect_identical(cobylaTest$iter, cobylaControl$iterations) expect_identical(cobylaTest$convergence, cobylaControl$status) expect_identical(cobylaTest$message, cobylaControl$message) # Test BOBYQA algorithm bobyqaTest <- bobyqa(c(0, 0), rbf, lower = c(0, 0), upper = c(0.5, 0.5)) bobyqaControl <- nloptr(x0 = c(0, 0), eval_f = rbf, lb = c(0, 0), ub = c(0.5, 0.5), opts = list(algorithm = "NLOPT_LN_BOBYQA", xtol_rel = 1e-6, maxeval = 1000L)) expect_identical(bobyqaTest$par, bobyqaControl$solution) expect_identical(bobyqaTest$value, bobyqaControl$objective) expect_identical(bobyqaTest$iter, bobyqaControl$iterations) expect_identical(bobyqaTest$convergence, bobyqaControl$status) expect_identical(bobyqaTest$message, bobyqaControl$message) # Test NEWUOA algorithm newuoaTest <- newuoa(c(1, 2), rbf) newuoaControl <- nloptr(x0 = c(1, 2), eval_f = rbf, opts = list(algorithm = "NLOPT_LN_NEWUOA", xtol_rel = 1e-6, maxeval = 1000L)) expect_identical(newuoaTest$par, newuoaControl$solution) expect_identical(newuoaTest$value, newuoaControl$objective) expect_identical(newuoaTest$iter, newuoaControl$iterations) expect_identical(newuoaTest$convergence, newuoaControl$status) expect_identical(newuoaTest$message, newuoaControl$message) nloptr/tools/0000755000176200001440000000000014763300100012722 5ustar liggesusersnloptr/tools/cmake_config.sh0000755000176200001440000000233214763300100015666 0ustar liggesusers#! /bin/sh #### CMAKE CONFIGURATION #### CMAKE_BIN="" if test -z "$CMAKE_BIN"; then # Look for a cmake3 binary in the current path CMAKE_BIN=`which cmake3 2>/dev/null` fi if test -z "$CMAKE_BIN"; then # Look for a cmake binary in the current path CMAKE_BIN=`which cmake 2>/dev/null` fi if test -z "$CMAKE_BIN"; then # Check for a MacOS specific path CMAKE_BIN=`which /Applications/CMake.app/Contents/bin/cmake 2>/dev/null` fi if test -z "$CMAKE_BIN"; then echo "" echo "------------------ CMAKE NOT FOUND --------------------" echo "" echo "CMake was not found on the PATH. Please install CMake:" echo "" echo " - sudo yum install cmake (Fedora/CentOS; inside a terminal)" echo " - sudo apt install cmake (Debian/Ubuntu; inside a terminal)." echo " - sudo pacman -S cmake (Arch Linux; inside a terminal)." echo " - brew install --cask cmake (MacOS; inside a terminal with Homebrew)" echo " - sudo port install cmake (MacOS; inside a terminal with MacPorts)" echo "" echo "Alternatively install CMake from: " echo "" echo "-------------------------------------------------------" echo "" exit 1 fi echo set CMAKE_BIN=$CMAKE_BIN nloptr/tools/winlibs.R0000644000176200001440000000047714351106341014530 0ustar liggesusers# Build against mingw-w64 build of nlopt if(!file.exists("../windows/nlopt-2.7.1/include/nlopt.hpp")){ download.file("https://github.com/rwinlib/nlopt/archive/v2.7.1.zip", "lib.zip", quiet = TRUE) dir.create("../windows", showWarnings = FALSE) unzip("lib.zip", exdir = "../windows") unlink("lib.zip") } nloptr/tools/cmake_call.sh0000755000176200001440000000211314763300100015331 0ustar liggesusers#! /bin/sh CMAKE_BIN=$1 : ${R_HOME=$(R RHOME)} RSCRIPT_BIN=${R_HOME}/bin/Rscript NCORES=`${RSCRIPT_BIN} -e "cat(min(2, parallel::detectCores(logical = FALSE), na.rm=TRUE))"` cd src # Compile NLOpt from source sh ./scripts/nlopt_download.sh ${RSCRIPT_BIN} dot() { file=$1; shift; . "$file"; } dot ./scripts/r_config.sh "" ${RSCRIPT_BIN} --vanilla -e 'getRversion() > "4.0.0"' | grep TRUE > /dev/null if [ $? -eq 0 ]; then CMAKE_ADD_AR="-D CMAKE_AR=${AR}" CMAKE_ADD_RANLIB="-D CMAKE_RANLIB=${RANLIB}" else CMAKE_ADD_AR="" CMAKE_ADD_RANLIB="" fi mkdir nlopt-build mkdir nlopt cd nlopt-build ${CMAKE_BIN} \ -D BUILD_SHARED_LIBS=OFF \ -D CMAKE_BUILD_TYPE=Release \ -D CMAKE_INSTALL_PREFIX=../nlopt \ -D NLOPT_CXX=ON \ -D NLOPT_GUILE=OFF \ -D NLOPT_MATLAB=OFF \ -D NLOPT_OCTAVE=OFF \ -D NLOPT_PYTHON=OFF \ -D NLOPT_SWIG=OFF \ -D NLOPT_TESTS=OFF \ ${CMAKE_ADD_AR} ${CMAKE_ADD_RANLIB} ../nlopt-src make -j${NCORES} make install cd .. lib_folder=`ls -d nlopt/lib*` echo "Moving ${lib_folder} to nlopt/lib" mv ${lib_folder} nlopt/lib # Cleanup sh ./scripts/nlopt_cleanup.sh nloptr/README.md0000644000176200001440000001116514765070675013074 0ustar liggesusers # [**nloptr**](https://astamm.github.io/nloptr/) [![R-CMD-check](https://github.com/astamm/nloptr/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/astamm/nloptr/actions/workflows/R-CMD-check.yaml) [![Codecov test coverage](https://codecov.io/gh/astamm/nloptr/graph/badge.svg)](https://app.codecov.io/gh/astamm/nloptr) [![pkgdown](https://github.com/astamm/nloptr/workflows/pkgdown/badge.svg)](https://github.com/astamm/nloptr/actions) [![CRAN status](https://www.r-pkg.org/badges/version/nloptr)](https://CRAN.R-project.org/package=nloptr) [**nloptr**](https://astamm.github.io/nloptr/) is an R interface to [NLopt](https://nlopt.readthedocs.io/en/latest/), a free/open-source library for nonlinear optimization started by Steven G. Johnson, providing a common interface for a number of different free optimization routines available online as well as original implementations of various other algorithms. It can be used to solve general nonlinear programming problems with nonlinear constraints and lower and upper bounds for the controls, such as $$ \min_{x \in \mathbb{R}^n} \quad f(x), $$ s.t. $g(x) \le 0$, $h(x) = 0$ and $\ell \le x \le u$. The [NLopt](https://nlopt.readthedocs.io/en/latest/) library is available under the GNU Lesser General Public License (LGPL), and the copyrights are owned by a variety of authors. See the [website](https://nlopt.readthedocs.io/en/latest/Citing_NLopt/) for information on how to cite NLopt and the algorithms you use. ## Installation ### Windows On Windows, for old versions of R (`R <= 4.1.x`), the *nlopt* `v2.7.1` from [rwinlib](https://github.com/rwinlib/nlopt) is used. For newer versions of R (`R >= 4.2.0`), the *nlopt* version from the corresponding `RTools` toolchain is used. ### Linux and macOS On Unix-like platforms, we use `pkg-config` to find a suitable system build of [NLopt](https://nlopt.readthedocs.io/en/latest/) (i.e. with version `>= 2.7.0`). - If it is found it is used. - Otherwise, [NLopt](https://nlopt.readthedocs.io/en/latest/) 2.10.0 is built from included sources using [CMake](https://cmake.org). In this case, a binary of [CMake](https://cmake.org) stored in environment variable `CMAKE_BIN` is searched on the `PATH` and, alternatively, on a macOS-specific location. If that variable cannot be set, install will abort suggesting ways of installing [CMake](https://cmake.org). The minimal version requirement on `cmake` is `>= 3.2.0`. ### Installing [CMake](https://cmake.org) (macOS and Linux only) Minimal version requirement for `cmake` is `3.2.0`. You can install [CMake](https://cmake.org) by following [CMake installation instructions](https://cmake.org/resources/). The important thing is that you add the [CMake](https://cmake.org) binary to your `PATH`: - On macOS, you can install [CMake](https://cmake.org) and then run it. In the menu bar, there is an item *How to Install For Command Line Use* which you can click on to have proper instructions on how to update your `PATH`. Note that the location of the [CMake](https://cmake.org) binary is always `/Applications/CMake.app/Contents/bin/cmake`. Hence, [**nloptr**](https://astamm.github.io/nloptr/) knows where to find it even if you do not update your `PATH`. - On Linux, it will be automatically added unless you specifically change the default installation directory before building [CMake](https://cmake.org). Alternatively, you can set an environment variable `CMAKE_BIN` pointing to a [CMake](https://cmake.org) binary of your liking on your computer for [**nloptr**](https://astamm.github.io/nloptr/) to use. ### Installing [**nloptr**](https://astamm.github.io/nloptr/) You can install [**nloptr**](https://astamm.github.io/nloptr/) from CRAN using: ``` r install.packages("nloptr") ``` Alternatively, you can install the development version from GitHub: ``` r # install.packages("remotes") remotes::install_github("astamm/nloptr") ``` ## Acknowledgments I would like to express my sincere gratitude to [Avraham Adler](https://github.com/aadler), [Dirk Eddelbuettel](https://github.com/eddelbuettel), [Mikael Jagan](https://github.com/jaganmn), [Tomas Kalibera](https://github.com/kalibera), [Jeroen Ooms](https://github.com/jeroen) and [Jelmer Ypma](https://github.com/jyypma) for their contributions and the very instructive discussions about the pros and cons of various build strategies in R packages. ## Reference Steven G. Johnson, The NLopt nonlinear-optimization package, nloptr/build/0000755000176200001440000000000014765523731012704 5ustar liggesusersnloptr/build/vignette.rds0000644000176200001440000000030214765523731015236 0ustar liggesusersb```b`aaf`b2 1# '/() MAaȠrCgIq*  :ּb4.y) 3G;<E T [fN*ސ89 d Bw(,/׃ @?{49'ݣ\)%ziE@ wVvnloptr/configure0000755000176200001440000037705714765523732013540 0ustar liggesusers#! /bin/sh # Guess values for system-dependent variables and create Makefiles. # Generated by GNU Autoconf 2.72 for nloptr 2.0.0. # # # Copyright (C) 1992-1996, 1998-2017, 2020-2023 Free Software Foundation, # Inc. # # # This configure script is free software; the Free Software Foundation # gives unlimited permission to copy, distribute and modify it. ## -------------------- ## ## M4sh Initialization. ## ## -------------------- ## # Be more Bourne compatible DUALCASE=1; export DUALCASE # for MKS sh if test ${ZSH_VERSION+y} && (emulate sh) >/dev/null 2>&1 then : emulate sh NULLCMD=: # Pre-4.2 versions of Zsh do word splitting on ${1+"$@"}, which # is contrary to our usage. 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"write failure creating $CONFIG_STATUS" "$LINENO" 5 # configure is writing to config.log, and then calls config.status. # config.status does its own redirection, appending to config.log. # Unfortunately, on DOS this fails, as config.log is still kept open # by configure, so config.status won't be able to write to it; its # output is simply discarded. So we exec the FD to /dev/null, # effectively closing config.log, so it can be properly (re)opened and # appended to by config.status. When coming back to configure, we # need to make the FD available again. if test "$no_create" != yes; then ac_cs_success=: ac_config_status_args= test "$silent" = yes && ac_config_status_args="$ac_config_status_args --quiet" exec 5>/dev/null $SHELL $CONFIG_STATUS $ac_config_status_args || ac_cs_success=false exec 5>>config.log # Use ||, not &&, to avoid exiting from the if with $? = 1, which # would make configure fail if this is the last instruction. $ac_cs_success || as_fn_exit 1 fi if test -n "$ac_unrecognized_opts" && test "$enable_option_checking" != no; then { printf "%s\n" "$as_me:${as_lineno-$LINENO}: WARNING: unrecognized options: $ac_unrecognized_opts" >&5 printf "%s\n" "$as_me: WARNING: unrecognized options: $ac_unrecognized_opts" >&2;} fi nloptr/man/0000755000176200001440000000000014633255630012352 5ustar liggesusersnloptr/man/neldermead.Rd0000644000176200001440000000503114472612401014732 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/nm.R \name{neldermead} \alias{neldermead} \title{Nelder-Mead Simplex} \usage{ neldermead( x0, fn, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ... ) } \arguments{ \item{x0}{starting point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{lower, upper}{lower and upper bound constraints.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ An implementation of almost the original Nelder-Mead simplex algorithm. } \details{ Provides explicit support for bound constraints, using essentially the method proposed in Box. Whenever a new point would lie outside the bound constraints the point is moved back exactly onto the constraint. } \note{ The author of NLopt would tend to recommend the Subplex method instead. } \examples{ # Fletcher and Powell's helic valley fphv <- function(x) 100*(x[3] - 10*atan2(x[2], x[1])/(2*pi))^2 + (sqrt(x[1]^2 + x[2]^2) - 1)^2 +x[3]^2 x0 <- c(-1, 0, 0) neldermead(x0, fphv) # 1 0 0 # Powell's Singular Function (PSF) psf <- function(x) (x[1] + 10*x[2])^2 + 5*(x[3] - x[4])^2 + (x[2] - 2*x[3])^4 + 10*(x[1] - x[4])^4 x0 <- c(3, -1, 0, 1) neldermead(x0, psf) # 0 0 0 0, needs maximum number of function calls \dontrun{ # Bounded version of Nelder-Mead rosenbrock <- function(x) { ## Rosenbrock Banana function 100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2 + 100 * (x[3] - x[2]^2)^2 + (1 - x[2])^2 } lower <- c(-Inf, 0, 0) upper <- c( Inf, 0.5, 1) x0 <- c(0, 0.1, 0.1) S <- neldermead(c(0, 0.1, 0.1), rosenbrock, lower, upper, nl.info = TRUE) # $xmin = c(0.7085595, 0.5000000, 0.2500000) # $fmin = 0.3353605} } \references{ J. A. Nelder and R. Mead, ``A simplex method for function minimization,'' The Computer Journal 7, p. 308-313 (1965). M. J. Box, ``A new method of constrained optimization and a comparison with other methods,'' Computer J. 8 (1), 42-52 (1965). } \seealso{ \code{dfoptim::nmk} } \author{ Hans W. Borchers } nloptr/man/nloptr.get.default.options.Rd0000644000176200001440000000245014351106341020042 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/nloptr.get.default.options.R \name{nloptr.get.default.options} \alias{nloptr.get.default.options} \title{Return a data.frame with all the options that can be supplied to nloptr.} \usage{ nloptr.get.default.options() } \value{ The return value contains a \code{data.frame} with the following elements \item{name}{name of the option} \item{type}{type (numeric, logical, integer, character)} \item{possible_values}{string explaining the values the option can take} \item{default}{default value of the option (as a string)} \item{is_termination_condition}{is this option part of the termination conditions?} \item{description}{description of the option (taken from NLopt website if it's an option that is passed on to NLopt).} } \description{ This function returns a data.frame with all the options that can be supplied to \code{\link[nloptr:nloptr]{nloptr}}. The data.frame contains the default values of the options and an explanation. A user-friendly way to show these options is by using the function \code{\link[nloptr:nloptr.print.options]{nloptr.print.options}}. } \seealso{ \code{\link[nloptr:nloptr]{nloptr}} \code{\link[nloptr:nloptr.print.options]{nloptr.print.options}} } \author{ Jelmer Ypma } \keyword{interface} \keyword{optimize} nloptr/man/mlsl.Rd0000644000176200001440000000757714633255630013630 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mlsl.R \name{mlsl} \alias{mlsl} \title{Multi-level Single-linkage} \usage{ mlsl( x0, fn, gr = NULL, lower, upper, local.method = "LBFGS", low.discrepancy = TRUE, nl.info = FALSE, control = list(), ... ) } \arguments{ \item{x0}{initial point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{gr}{gradient of function \code{fn}; will be calculated numerically if not specified.} \item{lower, upper}{lower and upper bound constraints.} \item{local.method}{only \code{BFGS} for the moment.} \item{low.discrepancy}{logical; shall a low discrepancy variation be used.} \item{nl.info}{logical; shall the original \acronym{NLopt} info be shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by \acronym{NLopt} and giving additional information.} } \description{ The \dQuote{Multi-Level Single-Linkage} (\acronym{MLSL}) algorithm for global optimization searches by a sequence of local optimizations from random starting points. A modification of \acronym{MLSL} is included using a low-discrepancy sequence (\acronym{LDS}) instead of pseudorandom numbers. } \details{ \acronym{MLSL} is a \sQuote{multistart} algorithm: it works by doing a sequence of local optimizations---using some other local optimization algorithm---from random or low-discrepancy starting points. MLSL is distinguished, however, by a `clustering' heuristic that helps it to avoid repeated searches of the same local optima and also has some theoretical guarantees of finding all local optima in a finite number of local minimizations. The local-search portion of \acronym{MLSL} can use any of the other algorithms in \acronym{NLopt}, and, in particular, can use either gradient-based or derivative-free algorithms. For this wrapper only gradient-based \acronym{LBFGS} is available as local method. } \note{ If you don't set a stopping tolerance for your local-optimization algorithm, \acronym{MLSL} defaults to \code{ftol_rel = 1e-15} and \code{xtol_rel = 1e-7} for the local searches. } \examples{ ## Minimize the Hartmann 6-Dimensional function ## See https://www.sfu.ca/~ssurjano/hart6.html a <- c(1.0, 1.2, 3.0, 3.2) A <- matrix(c(10, 0.05, 3, 17, 3, 10, 3.5, 8, 17, 17, 1.7, 0.05, 3.5, 0.1, 10, 10, 1.7, 8, 17, 0.1, 8, 14, 8, 14), nrow = 4) B <- matrix(c(.1312, .2329, .2348, .4047, .1696, .4135, .1451, .8828, .5569, .8307, .3522, .8732, .0124, .3736, .2883, .5743, .8283, .1004, .3047, .1091, .5886, .9991, .6650, .0381), nrow = 4) hartmann6 <- function(x, a, A, B) { fun <- 0 for (i in 1:4) { fun <- fun - a[i] * exp(-sum(A[i, ] * (x - B[i, ]) ^ 2)) } fun } ## The function has a global minimum of -3.32237 at ## (0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573) S <- mlsl(x0 = rep(0, 6), hartmann6, lower = rep(0, 6), upper = rep(1, 6), nl.info = TRUE, control = list(xtol_rel = 1e-8, maxeval = 1000), a = a, A = A, B = B) } \references{ A. H. G. Rinnooy Kan and G. T. Timmer, \dQuote{Stochastic global optimization methods} Mathematical Programming, vol. 39, p. 27-78 (1987). Sergei Kucherenko and Yury Sytsko, \dQuote{Application of deterministic low-discrepancy sequences in global optimization}, Computational Optimization and Applications, vol. 30, p. 297-318 (2005). } \seealso{ \code{\link{direct}} } \author{ Hans W. Borchers } nloptr/man/slsqp.Rd0000644000176200001440000000751714633255630014015 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/slsqp.R \name{slsqp} \alias{slsqp} \title{Sequential Quadratic Programming (SQP)} \usage{ slsqp( x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, heq = NULL, heqjac = NULL, nl.info = FALSE, control = list(), deprecatedBehavior = TRUE, ... ) } \arguments{ \item{x0}{starting point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{gr}{gradient of function \code{fn}; will be calculated numerically if not specified.} \item{lower, upper}{lower and upper bound constraints.} \item{hin}{function defining the inequality constraints, that is \code{hin <= 0} for all components. This is new behavior in line with the rest of the \code{nloptr} arguments. To use the old behavior, please set \code{deprecatedBehavior} to \code{TRUE}.} \item{hinjac}{Jacobian of function \code{hin}; will be calculated numerically if not specified.} \item{heq}{function defining the equality constraints, that is \code{heq = 0} for all components.} \item{heqjac}{Jacobian of function \code{heq}; will be calculated numerically if not specified.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{deprecatedBehavior}{logical; if \code{TRUE} (default for now), the old behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} instead of \eqn{\le 0}. This will be reversed in a future release and eventually removed.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 1) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ Sequential (least-squares) quadratic programming (SQP) algorithm for nonlinearly constrained, gradient-based optimization, supporting both equality and inequality constraints. } \details{ The algorithm optimizes successive second-order (quadratic/least-squares) approximations of the objective function (via BFGS updates), with first-order (affine) approximations of the constraints. } \note{ See more infos at \url{https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/}. } \examples{ ## Solve the Hock-Schittkowski problem no. 100 with analytic gradients ## See https://apmonitor.com/wiki/uploads/Apps/hs100.apm x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} hin.hs100 <- function(x) {c( 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - 11 * x[7]) } S <- slsqp(x0.hs100, fn = fn.hs100, # no gradients and jacobians provided hin = hin.hs100, nl.info = TRUE, control = list(xtol_rel = 1e-8, check_derivatives = TRUE), deprecatedBehavior = FALSE) ## The optimum value of the objective function should be 680.6300573 ## A suitable parameter vector is roughly ## (2.330, 1.9514, -0.4775, 4.3657, -0.6245, 1.0381, 1.5942) S } \references{ Dieter Kraft, ``A software package for sequential quadratic programming'', Technical Report DFVLR-FB 88-28, Institut fuer Dynamik der Flugsysteme, Oberpfaffenhofen, July 1988. } \seealso{ \code{alabama::auglag}, \code{Rsolnp::solnp}, \code{Rdonlp2::donlp2} } \author{ Hans W. Borchers } nloptr/man/nloptr.Rd0000644000176200001440000002253714614001640014155 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/nloptr.R \name{nloptr} \alias{nloptr} \title{R interface to NLopt} \usage{ nloptr( x0, eval_f, eval_grad_f = NULL, lb = NULL, ub = NULL, eval_g_ineq = NULL, eval_jac_g_ineq = NULL, eval_g_eq = NULL, eval_jac_g_eq = NULL, opts = list(), ... ) } \arguments{ \item{x0}{vector with starting values for the optimization.} \item{eval_f}{function that returns the value of the objective function. It can also return gradient information at the same time in a list with elements "objective" and "gradient" (see below for an example).} \item{eval_grad_f}{function that returns the value of the gradient of the objective function. Not all of the algorithms require a gradient.} \item{lb}{vector with lower bounds of the controls (use \code{-Inf} for controls without lower bound), by default there are no lower bounds for any of the controls.} \item{ub}{vector with upper bounds of the controls (use \code{Inf} for controls without upper bound), by default there are no upper bounds for any of the controls.} \item{eval_g_ineq}{function to evaluate (non-)linear inequality constraints that should hold in the solution. It can also return gradient information at the same time in a list with elements "constraints" and "jacobian" (see below for an example).} \item{eval_jac_g_ineq}{function to evaluate the Jacobian of the (non-)linear inequality constraints that should hold in the solution.} \item{eval_g_eq}{function to evaluate (non-)linear equality constraints that should hold in the solution. It can also return gradient information at the same time in a list with elements "constraints" and "jacobian" (see below for an example).} \item{eval_jac_g_eq}{function to evaluate the Jacobian of the (non-)linear equality constraints that should hold in the solution.} \item{opts}{list with options. The option "\code{algorithm}" is required. Check the \href{https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/}{NLopt website} for a full list of available algorithms. Other options control the termination conditions (\code{minf_max, ftol_rel, ftol_abs, xtol_rel,} \code{xtol_abs, maxeval, maxtime}). Default is \code{xtol_rel} = 1e-4. More information \href{https://nlopt.readthedocs.io/en/latest/NLopt_Introduction/#termination-conditions}{here}. #nolint A full description of all options is shown by the function \code{nloptr.print.options()}. Some algorithms with equality constraints require the option \code{local_opts}, which contains a list with an algorithm and a termination condition for the local algorithm. See \code{?`nloptr-package`} for an example. The option \code{print_level} controls how much output is shown during the optimization process. Possible values: \tabular{ll}{0 (default) \tab no output \cr 1 \tab show iteration number and value of objective function \cr 2 \tab 1 + show value of (in)equalities \cr 3 \tab 2 + show value of controls} The option \code{check_derivatives} (default = \code{FALSE}) can be used to run to compare the analytic gradients with finite difference approximations. The option \code{check_derivatives_print} (\code{'all'} (default), \code{'errors'}, \code{'none'}) controls the output of the derivative checker, if it is run, showing all comparisons, only those that resulted in an error, or none. The option \code{check_derivatives_tol} (default = 1e-04), determines when a difference between an analytic gradient and its finite difference approximation is flagged as an error.} \item{...}{arguments that will be passed to the user-defined objective and constraints functions.} } \value{ The return value contains a list with the inputs, and additional elements \item{call}{the call that was made to solve} \item{status}{integer value with the status of the optimization (0 is success)} \item{message}{more informative message with the status of the optimization} \item{iterations}{number of iterations that were executed} \item{objective}{value if the objective function in the solution} \item{solution}{optimal value of the controls} \item{version}{version of NLopt that was used} } \description{ nloptr is an R interface to NLopt, a free/open-source library for nonlinear optimization started by Steven G. Johnson, providing a common interface for a number of different free optimization routines available online as well as original implementations of various other algorithms. The NLopt library is available under the GNU Lesser General Public License (LGPL), and the copyrights are owned by a variety of authors. Most of the information here has been taken from \href{https://nlopt.readthedocs.io/en/latest/}{the NLopt website}, where more details are available. } \details{ NLopt addresses general nonlinear optimization problems of the form: \deqn{\min f(x)\quad x\in R^n}{min f(x) x in R^n} \deqn{\textrm{s.t. }\\ g(x) \leq 0\\ h(x) = 0\\ lb \leq x \leq ub}{ s.t. g(x) <= 0 h(x) = 0 lb <= x <= ub} where \eqn{f(x)} is the objective function to be minimized and \eqn{x} represents the \eqn{n} optimization parameters. This problem may optionally be subject to the bound constraints (also called box constraints), \eqn{lb} and \eqn{ub}. For partially or totally unconstrained problems the bounds can take \code{-Inf} or \code{Inf}. One may also optionally have \eqn{m} nonlinear inequality constraints (sometimes called a nonlinear programming problem), which can be specified in \eqn{g(x)}, and equality constraints that can be specified in \eqn{h(x)}. Note that not all of the algorithms in NLopt can handle constraints. } \note{ See \code{?`nloptr-package`} for an extended example. } \examples{ library('nloptr') ## Rosenbrock Banana function and gradient in separate functions eval_f <- function(x) { return(100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2) } eval_grad_f <- function(x) { return(c(-400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), 200 * (x[2] - x[1] * x[1]))) } # initial values x0 <- c(-1.2, 1) opts <- list("algorithm"="NLOPT_LD_LBFGS", "xtol_rel"=1.0e-8) # solve Rosenbrock Banana function res <- nloptr(x0=x0, eval_f=eval_f, eval_grad_f=eval_grad_f, opts=opts) print(res) ## Rosenbrock Banana function and gradient in one function # this can be used to economize on calculations eval_f_list <- function(x) { return( list( "objective" = 100 * (x[2] - x[1] * x[1]) ^ 2 + (1 - x[1]) ^ 2, "gradient" = c(-400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), 200 * (x[2] - x[1] * x[1])))) } # solve Rosenbrock Banana function using an objective function that # returns a list with the objective value and its gradient res <- nloptr(x0=x0, eval_f=eval_f_list, opts=opts) print(res) # Example showing how to solve the problem from the NLopt tutorial. # # min sqrt(x2) # s.t. x2 >= 0 # x2 >= (a1*x1 + b1)^3 # x2 >= (a2*x1 + b2)^3 # where # a1 = 2, b1 = 0, a2 = -1, b2 = 1 # # re-formulate constraints to be of form g(x) <= 0 # (a1*x1 + b1)^3 - x2 <= 0 # (a2*x1 + b2)^3 - x2 <= 0 library('nloptr') # objective function eval_f0 <- function(x, a, b) { return(sqrt(x[2])) } # constraint function eval_g0 <- function(x, a, b) { return((a*x[1] + b)^3 - x[2]) } # gradient of objective function eval_grad_f0 <- function(x, a, b) { return(c(0, .5/sqrt(x[2]))) } # Jacobian of constraint eval_jac_g0 <- function(x, a, b) { return(rbind(c(3*a[1]*(a[1]*x[1] + b[1])^2, -1.0), c(3*a[2]*(a[2]*x[1] + b[2])^2, -1.0))) } # functions with gradients in objective and constraint function # this can be useful if the same calculations are needed for # the function value and the gradient eval_f1 <- function(x, a, b) { return(list("objective"=sqrt(x[2]), "gradient"=c(0,.5/sqrt(x[2])))) } eval_g1 <- function(x, a, b) { return(list("constraints"=(a*x[1] + b)^3 - x[2], "jacobian"=rbind(c(3*a[1]*(a[1]*x[1] + b[1])^2, -1.0), c(3*a[2]*(a[2]*x[1] + b[2])^2, -1.0)))) } # define parameters a <- c(2,-1) b <- c(0, 1) # Solve using NLOPT_LD_MMA with gradient information supplied in separate # function. res0 <- nloptr(x0=c(1.234,5.678), eval_f=eval_f0, eval_grad_f=eval_grad_f0, lb = c(-Inf,0), ub = c(Inf,Inf), eval_g_ineq = eval_g0, eval_jac_g_ineq = eval_jac_g0, opts = list("algorithm"="NLOPT_LD_MMA"), a = a, b = b) print(res0) # Solve using NLOPT_LN_COBYLA without gradient information res1 <- nloptr(x0=c(1.234,5.678), eval_f=eval_f0, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g0, opts = list("algorithm" = "NLOPT_LN_COBYLA"), a = a, b = b) print(res1) # Solve using NLOPT_LD_MMA with gradient information in objective function res2 <- nloptr(x0=c(1.234, 5.678), eval_f=eval_f1, lb = c(-Inf, 0), ub = c(Inf, Inf), eval_g_ineq = eval_g1, opts = list("algorithm"="NLOPT_LD_MMA", "check_derivatives" = TRUE), a = a, b = b) print(res2) } \references{ Steven G. Johnson, The NLopt nonlinear-optimization package, \url{https://github.com/stevengj/nlopt} } \seealso{ \code{\link[nloptr:nloptr.print.options]{nloptr.print.options}} \code{\link[nloptr:check.derivatives]{check.derivatives}} \code{\link{optim}} \code{\link{nlm}} \code{\link{nlminb}} \code{Rsolnp::Rsolnp} \code{Rsolnp::solnp} } \author{ Steven G. Johnson and others (C code) \cr Jelmer Ypma (R interface) } \keyword{interface} \keyword{optimize} nloptr/man/auglag.Rd0000644000176200001440000001367614633255630014116 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/auglag.R \name{auglag} \alias{auglag} \title{Augmented Lagrangian Algorithm} \usage{ auglag( x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, heq = NULL, heqjac = NULL, localsolver = "COBYLA", localtol = 1e-06, ineq2local = FALSE, nl.info = FALSE, control = list(), deprecatedBehavior = TRUE, ... ) } \arguments{ \item{x0}{starting point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{gr}{gradient of the objective function; will be provided provided is \code{NULL} and the solver requires derivatives.} \item{lower, upper}{lower and upper bound constraints.} \item{hin, hinjac}{defines the inequality constraints, \code{hin(x) >= 0}} \item{heq, heqjac}{defines the equality constraints, \code{heq(x) = 0}.} \item{localsolver}{available local solvers: COBYLA, LBFGS, MMA, or SLSQP.} \item{localtol}{tolerance applied in the selected local solver.} \item{ineq2local}{logical; shall the inequality constraints be treated by the local solver?; not possible at the moment.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{deprecatedBehavior}{logical; if \code{TRUE} (default for now), the old behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} instead of \eqn{\le 0}. This will be reversed in a future release and eventually removed.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{global_solver}{the global NLOPT solver used.} \item{local_solver}{the local NLOPT solver used, LBFGS or COBYLA.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ The Augmented Lagrangian method adds additional terms to the unconstrained objective function, designed to emulate a Lagrangian multiplier. } \details{ This method combines the objective function and the nonlinear inequality/equality constraints (if any) in to a single function: essentially, the objective plus a `penalty' for any violated constraints. This modified objective function is then passed to another optimization algorithm with no nonlinear constraints. If the constraints are violated by the solution of this sub-problem, then the size of the penalties is increased and the process is repeated; eventually, the process must converge to the desired solution (if it exists). Since all of the actual optimization is performed in this subsidiary optimizer, the subsidiary algorithm that you specify determines whether the optimization is gradient-based or derivative-free. The local solvers available at the moment are \verb{COBYLA'' (for the derivative-free approach) and }LBFGS'', \verb{MMA'', or }SLSQP'' (for smooth functions). The tolerance for the local solver has to be provided. There is a variant that only uses penalty functions for equality constraints while inequality constraints are passed through to the subsidiary algorithm to be handled directly; in this case, the subsidiary algorithm must handle inequality constraints. (At the moment, this variant has been turned off because of problems with the NLOPT library.) } \note{ Birgin and Martinez provide their own free implementation of the method as part of the TANGO project; other implementations can be found in semi-free packages like LANCELOT. } \examples{ x0 <- c(1, 1) fn <- function(x) (x[1] - 2) ^ 2 + (x[2] - 1) ^ 2 hin <- function(x) 0.25 * x[1]^2 + x[2] ^ 2 - 1 # hin <= 0 heq <- function(x) x[1] - 2 * x[2] + 1 # heq = 0 gr <- function(x) nl.grad(x, fn) hinjac <- function(x) nl.jacobian(x, hin) heqjac <- function(x) nl.jacobian(x, heq) # with COBYLA auglag(x0, fn, gr = NULL, hin = hin, heq = heq, deprecatedBehavior = FALSE) # $par: 0.8228761 0.9114382 # $value: 1.393464 # $iter: 1001 auglag(x0, fn, gr = NULL, hin = hin, heq = heq, localsolver = "SLSQP", deprecatedBehavior = FALSE) # $par: 0.8228757 0.9114378 # $value: 1.393465 # $iter 184 ## Example from the alabama::auglag help page ## Parameters should be roughly (0, 0, 1) with an objective value of 1. fn <- function(x) (x[1] + 3 * x[2] + x[3]) ^ 2 + 4 * (x[1] - x[2]) ^ 2 heq <- function(x) x[1] + x[2] + x[3] - 1 # hin restated from alabama example to be <= 0. hin <- function(x) c(-6 * x[2] - 4 * x[3] + x[1] ^ 3 + 3, -x[1], -x[2], -x[3]) set.seed(12) auglag(runif(3), fn, hin = hin, heq = heq, localsolver= "lbfgs", deprecatedBehavior = FALSE) # $par: 4.861756e-08 4.732373e-08 9.999999e-01 # $value: 1 # $iter: 145 ## Powell problem from the Rsolnp::solnp help page ## Parameters should be roughly (-1.7171, 1.5957, 1.8272, -0.7636, -0.7636) ## with an objective value of 0.0539498478. x0 <- c(-2, 2, 2, -1, -1) fn1 <- function(x) exp(x[1] * x[2] * x[3] * x[4] * x[5]) eqn1 <-function(x) c(x[1] * x[1] + x[2] * x[2] + x[3] * x[3] + x[4] * x[4] + x[5] * x[5] - 10, x[2] * x[3] - 5 * x[4] * x[5], x[1] * x[1] * x[1] + x[2] * x[2] * x[2] + 1) auglag(x0, fn1, heq = eqn1, localsolver = "mma", deprecatedBehavior = FALSE) # $par: -1.7173645 1.5959655 1.8268352 -0.7636185 -0.7636185 # $value: 0.05394987 # $iter: 916 } \references{ Andrew R. Conn, Nicholas I. M. Gould, and Philippe L. Toint, ``A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds,'' SIAM J. Numer. Anal. vol. 28, no. 2, p. 545-572 (1991). E. G. Birgin and J. M. Martinez, ``Improving ultimate convergence of an augmented Lagrangian method," Optimization Methods and Software vol. 23, no. 2, p. 177-195 (2008). } \seealso{ \code{alabama::auglag}, \code{Rsolnp::solnp} } \author{ Hans W. Borchers } nloptr/man/varmetric.Rd0000644000176200001440000000427514472612401014637 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/varmetric.R \name{varmetric} \alias{varmetric} \title{Shifted Limited-memory Variable-metric} \usage{ varmetric( x0, fn, gr = NULL, rank2 = TRUE, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ... ) } \arguments{ \item{x0}{initial point for searching the optimum.} \item{fn}{objective function to be minimized.} \item{gr}{gradient of function \code{fn}; will be calculated numerically if not specified.} \item{rank2}{logical; if true uses a rank-2 update method, else rank-1.} \item{lower, upper}{lower and upper bound constraints.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of control parameters, see \code{nl.opts} for help.} \item{...}{further arguments to be passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ Shifted limited-memory variable-metric algorithm. } \details{ Variable-metric methods are a variant of the quasi-Newton methods, especially adapted to large-scale unconstrained (or bound constrained) minimization. } \note{ Based on L. Luksan's Fortran implementation of a shifted limited-memory variable-metric algorithm. } \examples{ flb <- function(x) { p <- length(x) sum(c(1, rep(4, p-1)) * (x - c(1, x[-p])^2)^2) } # 25-dimensional box constrained: par[24] is *not* at the boundary S <- varmetric(rep(3, 25), flb, lower=rep(2, 25), upper=rep(4, 25), nl.info = TRUE, control = list(xtol_rel=1e-8)) ## Optimal value of objective function: 368.105912874334 ## Optimal value of controls: 2 ... 2 2.109093 4 } \references{ J. Vlcek and L. Luksan, ``Shifted limited-memory variable metric methods for large-scale unconstrained minimization,'' J. Computational Appl. Math. 186, p. 365-390 (2006). } \seealso{ \code{\link{lbfgs}} } \author{ Hans W. Borchers } nloptr/man/check.derivatives.Rd0000644000176200001440000000455314472612401016243 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/check.derivatives.R \name{check.derivatives} \alias{check.derivatives} \title{Check analytic gradients of a function using finite difference approximations} \usage{ check.derivatives( .x, func, func_grad, check_derivatives_tol = 1e-04, check_derivatives_print = "all", func_grad_name = "grad_f", ... ) } \arguments{ \item{.x}{point at which the comparison is done.} \item{func}{function to be evaluated.} \item{func_grad}{function calculating the analytic gradients.} \item{check_derivatives_tol}{option determining when differences between the analytic gradient and its finite difference approximation are flagged as an error.} \item{check_derivatives_print}{option related to the amount of output. 'all' means that all comparisons are shown, 'errors' only shows comparisons that are flagged as an error, and 'none' shows the number of errors only.} \item{func_grad_name}{option to change the name of the gradient function that shows up in the output.} \item{...}{further arguments passed to the functions func and func_grad.} } \value{ The return value contains a list with the analytic gradient, its finite difference approximation, the relative errors, and vector comparing the relative errors to the tolerance. } \description{ This function compares the analytic gradients of a function with a finite difference approximation and prints the results of these checks. } \examples{ library('nloptr') # example with correct gradient f <- function(x, a) sum((x - a) ^ 2) f_grad <- function(x, a) 2 * (x - a) check.derivatives(.x = 1:10, func = f, func_grad = f_grad, check_derivatives_print = 'none', a = runif(10)) # example with incorrect gradient f_grad <- function(x, a) 2 * (x - a) + c(0, 0.1, rep(0, 8)) check.derivatives(.x = 1:10, func = f, func_grad = f_grad, check_derivatives_print = 'errors', a = runif(10)) # example with incorrect gradient of vector-valued function g <- function(x, a) c(sum(x - a), sum((x - a) ^ 2)) g_grad <- function(x, a) { rbind(rep(1, length(x)) + c(0, 0.01, rep(0, 8)), 2 * (x - a) + c(0, 0.1, rep(0, 8))) } check.derivatives(.x = 1:10, func = g, func_grad = g_grad, check_derivatives_print = 'all', a = runif(10)) } \seealso{ \code{\link[nloptr:nloptr]{nloptr}} } \author{ Jelmer Ypma } \keyword{interface} \keyword{optimize} nloptr/man/nloptr-package.Rd0000644000176200001440000001160214472612401015542 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/nloptr-package.R \docType{package} \name{nloptr-package} \alias{nloptr-package} \title{R interface to NLopt} \description{ nloptr is an R interface to NLopt, a free/open-source library for nonlinear optimization started by Steven G. Johnson, providing a common interface for a number of different free optimization routines available online as well as original implementations of various other algorithms. The NLopt library is available under the GNU Lesser General Public License (LGPL), and the copyrights are owned by a variety of authors. Most of the information here has been taken from \href{https://nlopt.readthedocs.io/en/latest/}{the NLopt website}, where more details are available. } \details{ NLopt addresses general nonlinear optimization problems of the form: \deqn{\min f(x)\quad x\in R^n}{min f(x) x in R^n} \deqn{\textrm{s.t. }\\ g(x) \leq 0\\ h(x) = 0\\ lb \leq x \leq ub}{ s.t. g(x) <= 0 h(x) = 0 lb <= x <= ub} where \eqn{f(x)} is the objective function to be minimized and \eqn{x} represents the \eqn{n} optimization parameters. This problem may optionally be subject to the bound constraints (also called box constraints), \eqn{lb} and \eqn{ub}. For partially or totally unconstrained problems the bounds can take \code{-Inf} or \code{Inf}. One may also optionally have \eqn{m} nonlinear inequality constraints (sometimes called a nonlinear programming problem), which can be specified in \eqn{g(x)}, and equality constraints that can be specified in \eqn{h(x)}. Note that not all of the algorithms in NLopt can handle constraints. An optimization problem can be solved with the general \code{nloptr} interface, or using one of the wrapper functions for the separate algorithms; \code{auglag}, \code{bobyqa}, \code{ccsaq}, \code{cobyla}, \code{crs2lm}, \code{direct}, \code{directL}, \code{isres}, \code{lbfgs}, \code{mlsl}, \code{mma}, \code{neldermead}, \code{newuoa}, \code{sbplx}, \code{slsqp}, \code{stogo}, \code{tnewton}, \code{varmetric}. \tabular{ll}{Package: \tab nloptr\cr Type: \tab Package\cr Version: \tab 2.0.3\cr Date: \tab 2022-05-26\cr License: \tab L-GPL >= 3\cr} } \note{ See ?nloptr for more examples. } \examples{ # Example problem, number 71 from the Hock-Schittkowsky test suite. # # \min_{x} x1 * x4 * (x1 + x2 + x3) + x3 # s.t. # x1 * x2 * x3 * x4 >= 25 # x1 ^ 2 + x2 ^ 2 + x3 ^ 2 + x4 ^ 2 = 40 # 1 <= x1, x2, x3, x4 <= 5 # # we re-write the inequality as # 25 - x1 * x2 * x3 * x4 <= 0 # # and the equality as # x1 ^ 2 + x2 ^ 2 + x3 ^ 2 + x4 ^ 2 - 40 = 0 # # x0 = (1, 5, 5, 1) # # optimal solution = (1.000000, 4.742999, 3.821151, 1.379408) library('nloptr') # # f(x) = x1 * x4 * (x1 + x2 + x3) + x3 # eval_f <- function(x) { list("objective" = x[1] * x[4] * (x[1] + x[2] + x[3]) + x[3], "gradient" = c(x[1] * x[4] + x[4] * (x[1] + x[2] + x[3]), x[1] * x[4], x[1] * x[4] + 1.0, x[1] * (x[1] + x[2] + x[3]))) } # constraint functions # inequalities eval_g_ineq <- function(x) { constr <- c(25 - x[1] * x[2] * x[3] * x[4]) grad <- c(-x[2] * x[3] * x[4], -x[1] * x[3] * x[4], -x[1] * x[2] * x[4], -x[1] * x[2] * x[3] ) list("constraints" = constr, "jacobian" = grad) } # equalities eval_g_eq <- function(x) { constr <- c(x[1] ^ 2 + x[2] ^ 2 + x[3] ^ 2 + x[4] ^ 2 - 40) grad <- c(2.0 * x[1], 2.0 * x[2], 2.0 * x[3], 2.0 * x[4]) list("constraints" = constr, "jacobian" = grad) } # initial values x0 <- c(1, 5, 5, 1) # lower and upper bounds of control lb <- c(1, 1, 1, 1) ub <- c(5, 5, 5, 5) local_opts <- list("algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1.0e-7) opts <- list("algorithm" = "NLOPT_LD_AUGLAG", "xtol_rel" = 1.0e-7, "maxeval" = 1000, "local_opts" = local_opts) res <- nloptr(x0 = x0, eval_f = eval_f, lb = lb, ub = ub, eval_g_ineq = eval_g_ineq, eval_g_eq = eval_g_eq, opts = opts) print(res) } \references{ Steven G. Johnson, The NLopt nonlinear-optimization package, \url{https://nlopt.readthedocs.io/en/latest/} } \seealso{ \code{\link{optim}} \code{\link{nlm}} \code{\link{nlminb}} \code{Rsolnp::Rsolnp} \code{Rsolnp::solnp} \code{\link{nloptr}} \code{\link{auglag}} \code{\link{bobyqa}} \code{\link{ccsaq}} \code{\link{cobyla}} \code{\link{crs2lm}} \code{\link{direct}} \code{\link{directL}} \code{\link{isres}} \code{\link{lbfgs}} \code{\link{mlsl}} \code{\link{mma}} \code{\link{neldermead}} \code{\link{newuoa}} \code{\link{sbplx}} \code{\link{slsqp}} \code{\link{stogo}} \code{\link{tnewton}} \code{\link{varmetric}} } \author{ Steven G. Johnson and others (C code) \cr Jelmer Ypma (R interface) \cr Hans W. Borchers (wrappers) } \keyword{interface} \keyword{internal} \keyword{optimize} nloptr/man/tnewton.Rd0000644000176200001440000000452214472612401014334 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tnewton.R \name{tnewton} \alias{tnewton} \title{Preconditioned Truncated Newton} \usage{ tnewton( x0, fn, gr = NULL, lower = NULL, upper = NULL, precond = TRUE, restart = TRUE, nl.info = FALSE, control = list(), ... ) } \arguments{ \item{x0}{starting point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{gr}{gradient of function \code{fn}; will be calculated numerically if not specified.} \item{lower, upper}{lower and upper bound constraints.} \item{precond}{logical; preset L-BFGS with steepest descent.} \item{restart}{logical; restarting L-BFGS with steepest descent.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 1) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ Truncated Newton methods, also called Newton-iterative methods, solve an approximating Newton system using a conjugate-gradient approach and are related to limited-memory BFGS. } \details{ Truncated Newton methods are based on approximating the objective with a quadratic function and applying an iterative scheme such as the linear conjugate-gradient algorithm. } \note{ Less reliable than Newton's method, but can handle very large problems. } \examples{ flb <- function(x) { p <- length(x) sum(c(1, rep(4, p - 1)) * (x - c(1, x[-p]) ^ 2) ^ 2) } # 25-dimensional box constrained: par[24] is *not* at boundary S <- tnewton(rep(3, 25L), flb, lower = rep(2, 25L), upper = rep(4, 25L), nl.info = TRUE, control = list(xtol_rel = 1e-8)) ## Optimal value of objective function: 368.105912874334 ## Optimal value of controls: 2 ... 2 2.109093 4 } \references{ R. S. Dembo and T. Steihaug, ``Truncated Newton algorithms for large-scale optimization,'' Math. Programming 26, p. 190-212 (1982). } \seealso{ \code{\link{lbfgs}} } \author{ Hans W. Borchers } nloptr/man/isres.Rd0000644000176200001440000000650514633255630013774 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/global.R \name{isres} \alias{isres} \title{Improved Stochastic Ranking Evolution Strategy} \usage{ isres( x0, fn, lower, upper, hin = NULL, heq = NULL, maxeval = 10000, pop.size = 20 * (length(x0) + 1), xtol_rel = 1e-06, nl.info = FALSE, deprecatedBehavior = TRUE, ... ) } \arguments{ \item{x0}{initial point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{lower, upper}{lower and upper bound constraints.} \item{hin}{function defining the inequality constraints, that is \code{hin <= 0} for all components.} \item{heq}{function defining the equality constraints, that is \code{heq = 0} for all components.} \item{maxeval}{maximum number of function evaluations.} \item{pop.size}{population size.} \item{xtol_rel}{stopping criterion for relative change reached.} \item{nl.info}{logical; shall the original \acronym{NLopt} info be shown.} \item{deprecatedBehavior}{logical; if \code{TRUE} (default for now), the old behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} instead of \eqn{\le 0}. This will be reversed in a future release and eventually removed.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ The Improved Stochastic Ranking Evolution Strategy (\acronym{ISRES}) is an algorithm for nonlinearly constrained global optimization, or at least semi-global, although it has heuristics to escape local optima. } \details{ The evolution strategy is based on a combination of a mutation rule---with a log-normal step-size update and exponential smoothing---and differential variation---a Nelder-Mead-like update rule). The fitness ranking is simply via the objective function for problems without nonlinear constraints, but when nonlinear constraints are included the stochastic ranking proposed by Runarsson and Yao is employed. This method supports arbitrary nonlinear inequality and equality constraints in addition to the bounds constraints. } \note{ The initial population size for CRS defaults to \eqn{20x(n+1)} in \eqn{n} dimensions, but this can be changed. The initial population must be at least \eqn{n+1}. } \examples{ ## Rosenbrock Banana objective function rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2} x0 <- c(-1.2, 1) lb <- c(-3, -3) ub <- c(3, 3) ## The function as written above has a minimum of 0 at (1, 1) isres(x0 = x0, fn = rbf, lower = lb, upper = ub) ## Now subject to the inequality that x[1] + x[2] <= 1.5 hin <- function(x) {x[1] + x[2] - 1.5} S <- isres(x0 = x0, fn = rbf, hin = hin, lower = lb, upper = ub, maxeval = 2e5L, deprecatedBehavior = FALSE) S sum(S$par) } \references{ Thomas Philip Runarsson and Xin Yao, ``Search biases in constrained evolutionary optimization,'' IEEE Trans. on Systems, Man, and Cybernetics Part C: Applications and Reviews, vol. 35 (no. 2), pp. 233-243 (2005). } \author{ Hans W. Borchers } nloptr/man/sbplx.Rd0000644000176200001440000000422014472612401013761 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/nm.R \name{sbplx} \alias{sbplx} \title{Subplex Algorithm} \usage{ sbplx( x0, fn, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ... ) } \arguments{ \item{x0}{starting point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{lower, upper}{lower and upper bound constraints.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ Subplex is a variant of Nelder-Mead that uses Nelder-Mead on a sequence of subspaces. } \details{ SUBPLEX is claimed to be much more efficient and robust than the original Nelder-Mead while retaining the latter's facility with discontinuous objectives. This implementation has explicit support for bound constraints via the method in the Box paper as described on the \code{neldermead} help page. } \note{ It is the request of Tom Rowan that reimplementations of his algorithm shall not use the name `subplex'. } \examples{ # Fletcher and Powell's helic valley fphv <- function(x) 100*(x[3] - 10*atan2(x[2], x[1])/(2*pi))^2 + (sqrt(x[1]^2 + x[2]^2) - 1)^2 +x[3]^2 x0 <- c(-1, 0, 0) sbplx(x0, fphv) # 1 0 0 # Powell's Singular Function (PSF) psf <- function(x) (x[1] + 10*x[2])^2 + 5*(x[3] - x[4])^2 + (x[2] - 2*x[3])^4 + 10*(x[1] - x[4])^4 x0 <- c(3, -1, 0, 1) sbplx(x0, psf, control = list(maxeval = Inf, ftol_rel = 1e-6)) # 0 0 0 0 (?) } \references{ T. Rowan, ``Functional Stability Analysis of Numerical Algorithms'', Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin, 1990. } \seealso{ \code{subplex::subplex} } nloptr/man/is.nloptr.Rd0000644000176200001440000000105614351106340014561 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/is.nloptr.R \name{is.nloptr} \alias{is.nloptr} \title{R interface to NLopt} \usage{ is.nloptr(x) } \arguments{ \item{x}{object to be tested.} } \value{ Logical. Return TRUE if all tests were passed, otherwise return FALSE or exit with Error. } \description{ is.nloptr preforms checks to see if a fully specified problem is supplied to nloptr. Mostly for internal use. } \seealso{ \code{\link[nloptr:nloptr]{nloptr}} } \author{ Jelmer Ypma } \keyword{interface} \keyword{optimize} nloptr/man/lbfgs.Rd0000644000176200001440000000470114472612401013732 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/lbfgs.R \name{lbfgs} \alias{lbfgs} \title{Low-storage BFGS} \usage{ lbfgs( x0, fn, gr = NULL, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ... ) } \arguments{ \item{x0}{initial point for searching the optimum.} \item{fn}{objective function to be minimized.} \item{gr}{gradient of function \code{fn}; will be calculated numerically if not specified.} \item{lower, upper}{lower and upper bound constraints.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of control parameters, see \code{nl.opts} for help.} \item{...}{further arguments to be passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ Low-storage version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. } \details{ The low-storage (or limited-memory) algorithm is a member of the class of quasi-Newton optimization methods. It is well suited for optimization problems with a large number of variables. One parameter of this algorithm is the number \code{m} of gradients to remember from previous optimization steps. NLopt sets \code{m} to a heuristic value by default. It can be changed by the NLopt function \code{set_vector_storage}. } \note{ Based on a Fortran implementation of the low-storage BFGS algorithm written by L. Luksan, and posted under the GNU LGPL license. } \examples{ flb <- function(x) { p <- length(x) sum(c(1, rep(4, p-1)) * (x - c(1, x[-p])^2)^2) } # 25-dimensional box constrained: par[24] is *not* at the boundary S <- lbfgs(rep(3, 25), flb, lower=rep(2, 25), upper=rep(4, 25), nl.info = TRUE, control = list(xtol_rel=1e-8)) ## Optimal value of objective function: 368.105912874334 ## Optimal value of controls: 2 ... 2 2.109093 4 } \references{ J. Nocedal, ``Updating quasi-Newton matrices with limited storage,'' Math. Comput. 35, 773-782 (1980). D. C. Liu and J. Nocedal, ``On the limited memory BFGS method for large scale optimization,'' Math. Programming 45, p. 503-528 (1989). } \seealso{ \code{\link{optim}} } \author{ Hans W. Borchers } nloptr/man/crs2lm.Rd0000644000176200001440000000630714633255630014051 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/global.R \name{crs2lm} \alias{crs2lm} \title{Controlled Random Search} \usage{ crs2lm( x0, fn, lower, upper, maxeval = 10000, pop.size = 10 * (length(x0) + 1), ranseed = NULL, xtol_rel = 1e-06, nl.info = FALSE, ... ) } \arguments{ \item{x0}{initial point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{lower, upper}{lower and upper bound constraints.} \item{maxeval}{maximum number of function evaluations.} \item{pop.size}{population size.} \item{ranseed}{prescribe seed for random number generator.} \item{xtol_rel}{stopping criterion for relative change reached.} \item{nl.info}{logical; shall the original \acronym{NLopt} info be shown.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by \acronym{NLopt} and giving additional information.} } \description{ The Controlled Random Search (\acronym{CRS}) algorithm (and in particular, the \acronym{CRS2} variant) with the `local mutation' modification. } \details{ The \acronym{CRS} algorithms are sometimes compared to genetic algorithms, in that they start with a random population of points, and randomly evolve these points by heuristic rules. In this case, the evolution somewhat resembles a randomized Nelder-Mead algorithm. The published results for \acronym{CRS} seem to be largely empirical. } \note{ The initial population size for CRS defaults to \eqn{10x(n+1)} in \eqn{n} dimensions, but this can be changed. The initial population must be at least \eqn{n+1}. } \examples{ ## Minimize the Hartmann 6-Dimensional function ## See https://www.sfu.ca/~ssurjano/hart6.html a <- c(1.0, 1.2, 3.0, 3.2) A <- matrix(c(10, 0.05, 3, 17, 3, 10, 3.5, 8, 17, 17, 1.7, 0.05, 3.5, 0.1, 10, 10, 1.7, 8, 17, 0.1, 8, 14, 8, 14), nrow = 4) B <- matrix(c(.1312, .2329, .2348, .4047, .1696, .4135, .1451, .8828, .5569, .8307, .3522, .8732, .0124, .3736, .2883, .5743, .8283, .1004, .3047, .1091, .5886, .9991, .6650, .0381), nrow = 4) hartmann6 <- function(x, a, A, B) { fun <- 0 for (i in 1:4) { fun <- fun - a[i] * exp(-sum(A[i, ] * (x - B[i, ]) ^ 2)) } fun } ## The function has a global minimum of -3.32237 at ## (0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573) S <- crs2lm(x0 = rep(0, 6), hartmann6, lower = rep(0, 6), upper = rep(1, 6), ranseed = 10L, nl.info = TRUE, xtol_rel=1e-8, maxeval = 10000, a = a, A = A, B = B) S } \references{ W. L. Price, ``Global optimization by controlled random search,'' J. Optim. Theory Appl. 40 (3), p. 333-348 (1983). P. Kaelo and M. M. Ali, ``Some variants of the controlled random search algorithm for global optimization,'' J. Optim. Theory Appl. 130 (2), 253-264 (2006). } nloptr/man/nloptr.print.options.Rd0000644000176200001440000000231314472612401016775 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/nloptr.print.options.R \name{nloptr.print.options} \alias{nloptr.print.options} \title{Print description of nloptr options} \usage{ nloptr.print.options(opts.show = NULL, opts.user = NULL) } \arguments{ \item{opts.show}{list or vector with names of options. A description will be shown for the options in this list. By default, a description of all options is shown.} \item{opts.user}{object containing user supplied options. This argument is optional. It is used when \code{nloptr.print.options} is called from \code{nloptr}. In that case options are listed if \code{print_options_doc} is set to \code{TRUE} when passing a minimization problem to \code{nloptr}.} } \description{ This function prints a list of all the options that can be set when solving a minimization problem using \code{nloptr}. } \examples{ library('nloptr') nloptr.print.options() nloptr.print.options(opts.show = c("algorithm", "check_derivatives")) opts <- list("algorithm"="NLOPT_LD_LBFGS", "xtol_rel"=1.0e-8) nloptr.print.options(opts.user = opts) } \seealso{ \code{\link[nloptr:nloptr]{nloptr}} } \author{ Jelmer Ypma } \keyword{interface} \keyword{optimize} nloptr/man/nl.opts.Rd0000644000176200001440000000206214351106340014224 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/nloptions.R \name{nl.opts} \alias{nl.opts} \title{Setting NL Options} \usage{ nl.opts(optlist = NULL) } \arguments{ \item{optlist}{list of options, see below.} } \value{ returns a list with default and changed options. } \description{ Sets and changes the NLOPT options. } \details{ The following options can be set (here with default values): \code{stopval = -Inf, # stop minimization at this value}\cr \code{xtol_rel = 1e-6, # stop on small optimization step}\cr \code{maxeval = 1000, # stop on this many function evaluations}\cr \code{ftol_rel = 0.0, # stop on change times function value}\cr \code{ftol_abs = 0.0, # stop on small change of function value}\cr \code{check_derivatives = FALSE} } \note{ There are more options that can be set for solvers in NLOPT. These cannot be set through their wrapper functions. To see the full list of options and algorithms, type \code{nloptr.print.options()}. } \examples{ nl.opts(list(xtol_rel = 1e-8, maxeval = 2000)) } \author{ Hans W. Borchers } nloptr/man/direct.Rd0000644000176200001440000001002114472715012014101 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/direct.R \name{direct} \alias{direct} \alias{directL} \title{DIviding RECTangles Algorithm for Global Optimization} \usage{ direct( fn, lower, upper, scaled = TRUE, original = FALSE, nl.info = FALSE, control = list(), ... ) directL( fn, lower, upper, randomized = FALSE, original = FALSE, nl.info = FALSE, control = list(), ... ) } \arguments{ \item{fn}{objective function that is to be minimized.} \item{lower, upper}{lower and upper bound constraints.} \item{scaled}{logical; shall the hypercube be scaled before starting.} \item{original}{logical; whether to use the original implementation by Gablonsky -- the performance is mostly similar.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{...}{additional arguments passed to the function.} \item{randomized}{logical; shall some randomization be used to decide which dimension to halve next in the case of near-ties.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ DIRECT is a deterministic search algorithm based on systematic division of the search domain into smaller and smaller hyperrectangles. The DIRECT_L makes the algorithm more biased towards local search (more efficient for functions without too many minima). } \details{ The DIRECT and DIRECT-L algorithms start by rescaling the bound constraints to a hypercube, which gives all dimensions equal weight in the search procedure. If your dimensions do not have equal weight, e.g. if you have a ``long and skinny'' search space and your function varies at about the same speed in all directions, it may be better to use unscaled variant of the DIRECT algorithm. The algorithms only handle finite bound constraints which must be provided. The original versions may include some support for arbitrary nonlinear inequality, but this has not been tested. The original versions do not have randomized or unscaled variants, so these options will be disregarded for these versions. } \note{ The DIRECT_L algorithm should be tried first. } \examples{ ### Minimize the Hartmann6 function hartmann6 <- function(x) { a <- c(1.0, 1.2, 3.0, 3.2) A <- matrix(c(10.0, 0.05, 3.0, 17.0, 3.0, 10.0, 3.5, 8.0, 17.0, 17.0, 1.7, 0.05, 3.5, 0.1, 10.0, 10.0, 1.7, 8.0, 17.0, 0.1, 8.0, 14.0, 8.0, 14.0), nrow=4, ncol=6) B <- matrix(c(.1312,.2329,.2348,.4047, .1696,.4135,.1451,.8828, .5569,.8307,.3522,.8732, .0124,.3736,.2883,.5743, .8283,.1004,.3047,.1091, .5886,.9991,.6650,.0381), nrow=4, ncol=6) fun <- 0 for (i in 1:4) { fun <- fun - a[i] * exp(-sum(A[i,] * (x - B[i,]) ^ 2)) } fun } S <- directL(hartmann6, rep(0, 6), rep(1, 6), nl.info = TRUE, control = list(xtol_rel = 1e-8, maxeval = 1000)) ## Number of Iterations....: 1000 ## Termination conditions: stopval: -Inf ## xtol_rel: 1e-08, maxeval: 1000, ftol_rel: 0, ftol_abs: 0 ## Number of inequality constraints: 0 ## Number of equality constraints: 0 ## Current value of objective function: -3.32236800687327 ## Current value of controls: ## 0.2016884 0.1500025 0.4768667 0.2753391 0.311648 0.6572931 } \references{ D. R. Jones, C. D. Perttunen, and B. E. Stuckmann, ``Lipschitzian optimization without the Lipschitz constant,'' J. Optimization Theory and Applications, vol. 79, p. 157 (1993). J. M. Gablonsky and C. T. Kelley, ``A locally-biased form of the DIRECT algorithm," J. Global Optimization, vol. 21 (1), p. 27-37 (2001). } \seealso{ The \code{dfoptim} package will provide a pure R version of this algorithm. } \author{ Hans W. Borchers } nloptr/man/figures/0000755000176200001440000000000014351106340014004 5ustar liggesusersnloptr/man/figures/logo.png0000644000176200001440000005346714351106340015471 0ustar liggesusersPNG  IHDRX?iCCPicc8U]hU>+$΃Ԧ5lRфem,lAݝi&3i)>A['!j-P(G 3k~s ,[%,-:t} }-+*&¿ gPG݅ج8"eŲ]A b ;l õWϙ2_E,(ۈ#Zsێ<5)"E6N#ӽEkۃO0}*rUt.iei #]r >cU{t7+ԙg߃xuWB_-%=^ t0uvW9 %/VBW'_tMۓP\>@y0`D i|[` hh)Tj0B#ЪhU# ~yhu fp#1I/I"0! 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Zertchaninov and K. Madsen, ``A C++ Programme for Global Optimization,'' IMM-REP-1998-04, Department of Mathematical Modelling, Technical University of Denmark. } \author{ Hans W. Borchers } nloptr/man/cobyla.Rd0000644000176200001440000000700114633255630014110 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/cobyla.R \name{cobyla} \alias{cobyla} \title{Constrained Optimization by Linear Approximations} \usage{ cobyla( x0, fn, lower = NULL, upper = NULL, hin = NULL, nl.info = FALSE, control = list(), deprecatedBehavior = TRUE, ... ) } \arguments{ \item{x0}{starting point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{lower, upper}{lower and upper bound constraints.} \item{hin}{function defining the inequality constraints, that is \code{hin>=0} for all components.} \item{nl.info}{logical; shall the original \acronym{NLopt} info be shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{deprecatedBehavior}{logical; if \code{TRUE} (default for now), the old behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} instead of \eqn{\le 0}. This will be reversed in a future release and eventually removed.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ \acronym{COBYLA} is an algorithm for derivative-free optimization with nonlinear inequality and equality constraints (but see below). } \details{ It constructs successive linear approximations of the objective function and constraints via a simplex of \eqn{n+1} points (in \eqn{n} dimensions), and optimizes these approximations in a trust region at each step. \acronym{COBYLA} supports equality constraints by transforming them into two inequality constraints. This functionality has not been added to the wrapper. To use \acronym{COBYLA} with equality constraints, please use the full \code{nloptr} invocation. } \note{ The original code, written in Fortran by Powell, was converted in C for the \acronym{SciPy} project. } \examples{ ## Solve the Hock-Schittkowski problem no. 100 with analytic gradients ## See https://apmonitor.com/wiki/uploads/Apps/hs100.apm x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} hin.hs100 <- function(x) {c( 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - 11 * x[7]) } S <- cobyla(x0.hs100, fn.hs100, hin = hin.hs100, nl.info = TRUE, control = list(xtol_rel = 1e-8, maxeval = 2000), deprecatedBehavior = FALSE) ## The optimum value of the objective function should be 680.6300573 ## A suitable parameter vector is roughly ## (2.330, 1.9514, -0.4775, 4.3657, -0.6245, 1.0381, 1.5942) S } \references{ M. J. D. Powell, ``A direct search optimization method that models the objective and constraint functions by linear interpolation,'' in Advances in Optimization and Numerical Analysis, eds. S. Gomez and J.-P. Hennart (Kluwer Academic: Dordrecht, 1994), p. 51-67. } \seealso{ \code{\link{bobyqa}}, \code{\link{newuoa}} } \author{ Hans W. Borchers } nloptr/man/nl.grad.Rd0000644000176200001440000000217714472612401014167 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/gradients.R \name{nl.grad} \alias{nl.grad} \alias{nl.jacobian} \title{Numerical Gradients and Jacobians} \usage{ nl.grad(x0, fn, heps = .Machine$double.eps^(1/3), ...) } \arguments{ \item{x0}{point as a vector where the gradient is to be calculated.} \item{fn}{scalar function of one or several variables.} \item{heps}{step size to be used.} \item{\dots}{additional arguments passed to the function.} } \value{ \code{grad} returns the gradient as a vector; \code{jacobian} returns the Jacobian as a matrix of usual dimensions. } \description{ Provides numerical gradients and Jacobians. } \details{ Both functions apply the ``central difference formula'' with step size as recommended in the literature. } \examples{ fn1 <- function(x) sum(x ^ 2) nl.grad(seq(0, 1, by = 0.2), fn1) ## [1] 0.0 0.4 0.8 1.2 1.6 2.0 nl.grad(rep(1, 5), fn1) ## [1] 2 2 2 2 2 fn2 <- function(x) c(sin(x), cos(x)) x <- (0:1) * 2 * pi nl.jacobian(x, fn2) ## [,1] [,2] ## [1,] 1 0 ## [2,] 0 1 ## [3,] 0 0 ## [4,] 0 0 } \author{ Hans W. Borchers } nloptr/man/mma.Rd0000644000176200001440000001023614633255630013415 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mma.R \name{mma} \alias{mma} \title{Method of Moving Asymptotes} \usage{ mma( x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, nl.info = FALSE, control = list(), deprecatedBehavior = TRUE, ... ) } \arguments{ \item{x0}{starting point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{gr}{gradient of function \code{fn}; will be calculated numerically if not specified.} \item{lower, upper}{lower and upper bound constraints.} \item{hin}{function defining the inequality constraints, that is \code{hin <= 0} for all components.} \item{hinjac}{Jacobian of function \code{hin}; will be calculated numerically if not specified.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{deprecatedBehavior}{logical; if \code{TRUE} (default for now), the old behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} instead of \eqn{\le 0}. This will be reversed in a future release and eventually removed.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 1) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ Globally-convergent method-of-moving-asymptotes (\acronym{MMA}) algorithm for gradient-based local optimization, including nonlinear inequality constraints (but not equality constraints). } \details{ This is an improved \acronym{CCSA} ("conservative convex separable approximation") variant of the original \acronym{MMA} algorithm published by Svanberg in 1987, which has become popular for topology optimization. } \note{ \dQuote{Globally convergent} does not mean that this algorithm converges to the global optimum; rather, it means that the algorithm is guaranteed to converge to some local minimum from any feasible starting point. } \examples{ # Solve the Hock-Schittkowski problem no. 100 with analytic gradients # See https://apmonitor.com/wiki/uploads/Apps/hs100.apm x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} hin.hs100 <- function(x) {c( 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - 11 * x[7]) } gr.hs100 <- function(x) { c( 2 * x[1] - 20, 10 * x[2] - 120, 4 * x[3] ^ 3, 6 * x[4] - 66, 60 * x[5] ^ 5, 14 * x[6] - 4 * x[7] - 10, 4 * x[7] ^ 3 - 4 * x[6] - 8) } hinjac.hs100 <- function(x) { matrix(c(4 * x[1], 12 * x[2] ^ 3, 1, 8 * x[4], 5, 0, 0, 7, 3, 20 * x[3], 1, -1, 0, 0, 23, 2 * x[2], 0, 0, 0, 12 * x[6], -8, 8 * x[1] - 3 * x[2], 2 * x[2] - 3 * x[1], 4 * x[3], 0, 0, 5, -11), nrow = 4, byrow = TRUE) } # The optimum value of the objective function should be 680.6300573 # A suitable parameter vector is roughly # (2.330, 1.9514, -0.4775, 4.3657, -0.6245, 1.0381, 1.5942) # Using analytic Jacobian S <- mma(x0.hs100, fn.hs100, gr = gr.hs100, hin = hin.hs100, hinjac = hinjac.hs100, nl.info = TRUE, control = list(xtol_rel = 1e-8), deprecatedBehavior = FALSE) # Using computed Jacobian S <- mma(x0.hs100, fn.hs100, hin = hin.hs100, nl.info = TRUE, control = list(xtol_rel = 1e-8), deprecatedBehavior = FALSE) } \references{ Krister Svanberg, \dQuote{A class of globally convergent optimization methods based on conservative convex separable approximations}, SIAM J. Optim. 12 (2), p. 555-573 (2002). } \seealso{ \code{\link{slsqp}} } \author{ Hans W. Borchers } nloptr/man/ccsaq.Rd0000644000176200001440000001003614633255630013733 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/ccsaq.R \name{ccsaq} \alias{ccsaq} \title{Conservative Convex Separable Approximation with Affine Approximation plus Quadratic Penalty} \usage{ ccsaq( x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, nl.info = FALSE, control = list(), deprecatedBehavior = TRUE, ... ) } \arguments{ \item{x0}{starting point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{gr}{gradient of function \code{fn}; will be calculated numerically if not specified.} \item{lower, upper}{lower and upper bound constraints.} \item{hin}{function defining the inequality constraints, that is \code{hin>=0} for all components.} \item{hinjac}{Jacobian of function \code{hin}; will be calculated numerically if not specified.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{deprecatedBehavior}{logical; if \code{TRUE} (default for now), the old behavior of the Jacobian function is used, where the equality is \eqn{\ge 0} instead of \eqn{\le 0}. This will be reversed in a future release and eventually removed.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 1) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ This is a variant of CCSA ("conservative convex separable approximation") which, instead of constructing local MMA approximations, constructs simple quadratic approximations (or rather, affine approximations plus a quadratic penalty term to stay conservative) } \note{ ``Globally convergent'' does not mean that this algorithm converges to the global optimum; it means that it is guaranteed to converge to some local minimum from any feasible starting point. } \examples{ ## Solve the Hock-Schittkowski problem no. 100 with analytic gradients ## See https://apmonitor.com/wiki/uploads/Apps/hs100.apm x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1) fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 + 3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 + x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]} hin.hs100 <- function(x) {c( 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127, 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282, 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196, 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] - 11 * x[7]) } gr.hs100 <- function(x) { c( 2 * x[1] - 20, 10 * x[2] - 120, 4 * x[3] ^ 3, 6 * x[4] - 66, 60 * x[5] ^ 5, 14 * x[6] - 4 * x[7] - 10, 4 * x[7] ^ 3 - 4 * x[6] - 8) } hinjac.hs100 <- function(x) { matrix(c(4 * x[1], 12 * x[2] ^ 3, 1, 8 * x[4], 5, 0, 0, 7, 3, 20 * x[3], 1, -1, 0, 0, 23, 2 * x[2], 0, 0, 0, 12 * x[6], -8, 8 * x[1] - 3 * x[2], 2 * x[2] - 3 * x[1], 4 * x[3], 0, 0, 5, -11), nrow = 4, byrow = TRUE) } ## The optimum value of the objective function should be 680.6300573 ## A suitable parameter vector is roughly ## (2.330, 1.9514, -0.4775, 4.3657, -0.6245, 1.0381, 1.5942) # Results with exact Jacobian S <- ccsaq(x0.hs100, fn.hs100, gr = gr.hs100, hin = hin.hs100, hinjac = hinjac.hs100, nl.info = TRUE, control = list(xtol_rel = 1e-8), deprecatedBehavior = FALSE) # Results without Jacobian S <- ccsaq(x0.hs100, fn.hs100, hin = hin.hs100, nl.info = TRUE, control = list(xtol_rel = 1e-8), deprecatedBehavior = FALSE) } \references{ Krister Svanberg, ``A class of globally convergent optimization methods based on conservative convex separable approximations,'' SIAM J. Optim. 12 (2), p. 555-573 (2002). } \seealso{ \code{\link{mma}} } nloptr/man/newuoa.Rd0000644000176200001440000000372014633255630014141 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/cobyla.R \name{newuoa} \alias{newuoa} \title{New Unconstrained Optimization with quadratic Approximation} \usage{ newuoa(x0, fn, nl.info = FALSE, control = list(), ...) } \arguments{ \item{x0}{starting point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{nl.info}{logical; shall the original \acronym{NLopt} info be shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by NLopt and giving additional information.} } \description{ \acronym{NEWUOA} solves quadratic subproblems in a spherical trust region via a truncated conjugate-gradient algorithm. For bound-constrained problems, \acronym{BOBYQA} should be used instead, as Powell developed it as an enhancement thereof for bound constraints. } \details{ This is an algorithm derived from the \acronym{NEWUOA} Fortran subroutine of Powell, converted to C and modified for the \acronym{NLopt} stopping criteria. } \note{ \acronym{NEWUOA} may be largely superseded by \acronym{BOBYQA}. } \examples{ ## Rosenbrock Banana function rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2} S <- newuoa(c(1, 2), rbf) ## The function as written above has a minimum of 0 at (1, 1) S } \references{ M. J. D. Powell. ``The BOBYQA algorithm for bound constrained optimization without derivatives,'' Department of Applied Mathematics and Theoretical Physics, Cambridge England, technical reportNA2009/06 (2009). } \seealso{ \code{\link{bobyqa}}, \code{\link{cobyla}} } \author{ Hans W. Borchers } nloptr/man/bobyqa.Rd0000644000176200001440000000423414633255630014121 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/cobyla.R \name{bobyqa} \alias{bobyqa} \title{Bound Optimization by Quadratic Approximation} \usage{ bobyqa( x0, fn, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ... ) } \arguments{ \item{x0}{starting point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{lower, upper}{lower and upper bound constraints.} \item{nl.info}{logical; shall the original \acronym{NLopt} info be shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{...}{additional arguments passed to the function.} } \value{ List with components: \item{par}{the optimal solution found so far.} \item{value}{the function value corresponding to \code{par}.} \item{iter}{number of (outer) iterations, see \code{maxeval}.} \item{convergence}{integer code indicating successful completion (> 0) or a possible error number (< 0).} \item{message}{character string produced by \acronym{NLopt} and giving additional information.} } \description{ \acronym{BOBYQA} performs derivative-free bound-constrained optimization using an iteratively constructed quadratic approximation for the objective function. } \details{ This is an algorithm derived from the \acronym{BOBYQA} Fortran subroutine of Powell, converted to C and modified for the \acronym{NLopt} stopping criteria. } \note{ Because \acronym{BOBYQA} constructs a quadratic approximation of the objective, it may perform poorly for objective functions that are not twice-differentiable. } \examples{ ## Rosenbrock Banana function rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2} ## The function as written above has a minimum of 0 at (1, 1) S <- bobyqa(c(0, 0), rbf) S ## Rosenbrock Banana function with both parameters constrained to [0, 0.5] S <- bobyqa(c(0, 0), rbf, lower = c(0, 0), upper = c(0.5, 0.5)) S } \references{ M. J. D. Powell. ``The BOBYQA algorithm for bound constrained optimization without derivatives,'' Department of Applied Mathematics and Theoretical Physics, Cambridge England, technical reportNA2009/06 (2009). } \seealso{ \code{\link{cobyla}}, \code{\link{newuoa}} } nloptr/man/print.nloptr.Rd0000644000176200001440000000172114472612401015305 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/print.nloptr.R \name{print.nloptr} \alias{print.nloptr} \title{Print results after running nloptr} \usage{ \method{print}{nloptr}(x, show.controls = TRUE, ...) } \arguments{ \item{x}{object containing result from minimization.} \item{show.controls}{Logical or vector with indices. Should we show the value of the control variables in the solution? If \code{show.controls} is a vector with indices, it is used to select which control variables should be shown. This can be useful if the model contains a set of parameters of interest and a set of nuisance parameters that are not of immediate interest.} \item{...}{further arguments passed to or from other methods.} } \description{ This function prints the nloptr object that holds the results from a minimization using \code{nloptr}. } \seealso{ \code{\link[nloptr:nloptr]{nloptr}} } \author{ Jelmer Ypma } \keyword{interface} \keyword{optimize} nloptr/DESCRIPTION0000644000176200001440000000635514765676562013337 0ustar liggesusersPackage: nloptr Type: Package Title: R Interface to NLopt Version: 2.2.1 Authors@R: c(person("Jelmer", "Ypma", role = "aut", email = "uctpjyy@ucl.ac.uk"), person(c("Steven", "G."), "Johnson", role = "aut", comment = "author of the NLopt C library"), person("Aymeric", "Stamm", role = c("ctb", "cre"), email = "aymeric.stamm@cnrs.fr", comment = c(ORCID = "0000-0002-8725-3654")), person(c("Hans", "W."), "Borchers", role = "ctb", email = "hwborchers@googlemail.com"), person("Dirk", "Eddelbuettel", role = "ctb", email = "edd@debian.org"), person("Brian", "Ripley", role = "ctb", comment = "build process on multiple OS"), person("Kurt", "Hornik", role = "ctb", comment = "build process on multiple OS"), person("Julien", "Chiquet", role = "ctb"), person("Avraham", "Adler", role = "ctb", email = "Avraham.Adler@gmail.com", comment = c(ORCID = "0000-0002-3039-0703")), person("Xiongtao", "Dai", role = "ctb"), person("Jeroen", "Ooms", role = "ctb", email = "jeroen@berkeley.edu"), person("Tomas", "Kalibera", role = "ctb"), person("Mikael", "Jagan", role = "ctb")) Description: Solve optimization problems using an R interface to NLopt. NLopt is a free/open-source library for nonlinear optimization, providing a common interface for a number of different free optimization routines available online as well as original implementations of various other algorithms. See for more information on the available algorithms. Building from included sources requires 'CMake'. On Linux and 'macOS', if a suitable system build of NLopt (2.7.0 or later) is found, it is used; otherwise, it is built from included sources via 'CMake'. On Windows, NLopt is obtained through 'rwinlib' for 'R <= 4.1.x' or grabbed from the appropriate toolchain for 'R >= 4.2.0'. License: LGPL (>= 3) SystemRequirements: cmake (>= 3.2.0) which is used only on Linux or macOS systems when no system build of nlopt (>= 2.7.0) can be found. Encoding: UTF-8 RoxygenNote: 7.3.2 Suggests: knitr, rmarkdown, covr, tinytest VignetteBuilder: knitr URL: https://github.com/astamm/nloptr, https://astamm.github.io/nloptr/ BugReports: https://github.com/astamm/nloptr/issues NeedsCompilation: yes UseLTO: yes Packaged: 2025-03-16 10:28:42 UTC; stamm-a Author: Jelmer Ypma [aut], Steven G. Johnson [aut] (author of the NLopt C library), Aymeric Stamm [ctb, cre] (), Hans W. Borchers [ctb], Dirk Eddelbuettel [ctb], Brian Ripley [ctb] (build process on multiple OS), Kurt Hornik [ctb] (build process on multiple OS), Julien Chiquet [ctb], Avraham Adler [ctb] (), Xiongtao Dai [ctb], Jeroen Ooms [ctb], Tomas Kalibera [ctb], Mikael Jagan [ctb] Maintainer: Aymeric Stamm Repository: CRAN Date/Publication: 2025-03-17 01:40:02 UTC

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