nloptr/0000755000176200001440000000000012367706057011605 5ustar liggesusersnloptr/inst/0000755000176200001440000000000012367224773012562 5ustar liggesusersnloptr/inst/CITATION0000644000176200001440000000141412367224754013716 0ustar liggesuserscitHeader("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:") citEntry(entry="Article", title = "The NLopt nonlinear-optimization package", author = personList(as.person("Steven G. Johnson")), year = "?", journal = "?", volume = "?", number = "?", pages = "?", textVersion = "Steven G. Johnson, The NLopt nonlinear-optimization package, http://ab-initio.mit.edu/nlopt" ) citFooter("The authors and appropriate citations for the specific optimization algorithms in NLopt are listed in the NLopt Algorithms page.") nloptr/inst/doc/0000755000176200001440000000000012367224773013327 5ustar liggesusersnloptr/inst/doc/nloptr.R0000644000176200001440000001655112367224773015000 0ustar liggesusers### R code from vignette source 'nloptr.Rnw' ################################################### ### code chunk number 1: setSweaveOptions ################################################### # 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)))) ################################################### ### code chunk number 2: installNLopt (eval = FALSE) ################################################### ## install.packages("nloptr") ################################################### ### code chunk number 3: testNLoptInstallation (eval = FALSE) ################################################### ## library('nloptr') ## ?nloptr ################################################### ### code chunk number 4: installNLoptRForge (eval = FALSE) ################################################### ## install.packages("nloptr",repos="http://R-Forge.R-project.org") ################################################### ### code chunk number 5: installNLoptRForgeSource (eval = FALSE) ################################################### ## install.packages("nloptr",type="source",repos="http://R-Forge.R-project.org") ################################################### ### code chunk number 6: loadLibrary ################################################### library(nloptr) ################################################### ### code chunk number 7: defineRosenbrockBanana ################################################### ## Rosenbrock Banana function eval_f <- function(x) { return( 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2 ) } ## Gradient of Rosenbrock Banana function 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]) ) ) } ################################################### ### code chunk number 8: setRosenbrockBananaInitialValues ################################################### # initial values x0 <- c( -1.2, 1 ) ################################################### ### code chunk number 9: setRosenbrockBananaOptions ################################################### opts <- list("algorithm"="NLOPT_LD_LBFGS", "xtol_rel"=1.0e-8) ################################################### ### code chunk number 10: solveRosenbrockBanana ################################################### # solve Rosenbrock Banana function res <- nloptr( x0=x0, eval_f=eval_f, eval_grad_f=eval_grad_f, opts=opts) ################################################### ### code chunk number 11: printRosenbrockBanana ################################################### print( res ) ################################################### ### code chunk number 12: defineRosenbrockBananaList ################################################### ## Rosenbrock Banana function and gradient in one function eval_f_list <- function(x) { common_term <- x[2] - x[1] * x[1] return( list( "objective" = 100 * common_term^2 + (1 - x[1])^2, "gradient" = c( -400 * x[1] * common_term - 2 * (1 - x[1]), 200 * common_term) ) ) } ################################################### ### code chunk number 13: solveRosenbrockBananaList ################################################### res <- nloptr( x0=x0, eval_f=eval_f_list, opts=opts) print( res ) ################################################### ### code chunk number 14: defineTutorialObjective ################################################### # objective function eval_f0 <- function( x, a, b ){ return( sqrt(x[2]) ) } # gradient of objective function eval_grad_f0 <- function( x, a, b ){ return( c( 0, .5/sqrt(x[2]) ) ) } ################################################### ### code chunk number 15: defineTutorialConstraints ################################################### # constraint function eval_g0 <- function( x, a, b ) { return( (a*x[1] + b)^3 - 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 ) ) ) } ################################################### ### code chunk number 16: defineTutorialParameters ################################################### # define parameters a <- c(2,-1) b <- c(0, 1) ################################################### ### code chunk number 17: 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 ) ################################################### ### code chunk number 18: 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 ) ################################################### ### code chunk number 19: derivativeCheckerDefineFunctions ################################################### g <- function( x, a ) { return( 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 ) { return( 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 ) ) ) } ################################################### ### code chunk number 20: derivativeCheckerPrint ################################################### res <- check.derivatives( .x=c(1,2), func=g, func_grad=g_grad, check_derivatives_print='all', a=c(.3, .8) ) ################################################### ### code chunk number 21: derivativeCheckerResult ################################################### res ################################################### ### code chunk number 22: printAllOptions ################################################### nloptr.print.options() nloptr/inst/doc/nloptr.pdf0000644000176200001440000100757712367224773015361 0ustar liggesusers%PDF-1.5 % 3 0 obj << /Length 3228 /Filter /FlateDecode >> stream xڵr]_Gj&\a/y$URv:I $~}m =m X={7o^rset m*2L-o?/ӭɗCޮL~34-}^,߽vn4)iH &Sݮ : .ˀۮ$Gd}ȿcjhHfn[A`smU#xϊ8Nrdջͪ#ymp-PH DwQZ}ˢA^h#zQ.# Ҁ>Q|Ug-{ǀ֛`ȸoAV&b67v->ڥDۺ%Sl xqǒ:s[BnӜ>Jlaqny߰!$imyo+p6Ϯ_Jy) L,m私H@\0s%V d0ߥB-w"UmʳtG3G?]䑳OR3x *Bo#zzkxDʀ7L1J #VJSA^NeM'ֲPb(8]W\U'B';ϸ=E,aC )JcUN7":ypo/edCJD#6j}iTSА4Ƅ2&`/k8vZ0|2"NF q21Jf[<)PH!Vf:{qm1H\Tu;-1Cӡ* `a# *F>xwnFE==S 9"# %XRpl1!C.3 ě1x|$枈#e[OArĊ+({AnI(&J/>dڟ+в16\ү" <'팿Yy1ګChrJkcuZnYz)޼z |Bs]d*d}d aebHt؃n~ [ b0.րpK?@P k%pvTMRX4\zXK監̀| |o o oT\OOg/#Ԟ_B2˓H&4xHӇ&VSu4]<5=l/]F.1\"|(UI2[{MXuZ7rEe҄'GgVVIJ%SlEd ͚n(sRyRW|NK?Mw;Hy5"})e|Y)C4=4/d<{^O&Goq0PƏLQnnIPЬG /:wo04rơ))fO8Jo(x)g8Bi@1+vJzp~(<_*E)c)+Aa_Kwk绗ai[j"z'c(1%P3"oS endstream endobj 2 0 obj << /Type /Page /Contents 3 0 R /Resources 1 0 R /MediaBox [0 0 595.276 841.89] /Parent 22 0 R >> endobj 1 0 obj << /Font << /F19 4 0 R /F44 5 0 R /F24 6 0 R /F20 7 0 R /F48 8 0 R /F53 9 0 R /F58 10 0 R /F59 11 0 R /F8 12 0 R /F10 13 0 R /F13 14 0 R /F9 15 0 R /F11 16 0 R /F7 17 0 R /F31 18 0 R /F26 19 0 R /F70 20 0 R /F27 21 0 R >> /ProcSet [ /PDF /Text ] >> endobj 25 0 obj << /Length 1958 /Filter /FlateDecode >> stream xYo6_!ڊIQa6l} C 8^cː&}wǣDLݖEy<w:zT̄rFReLUTN7#'&F?rXsgY~~~PFr#4JvesttHh'*FcWx/__ =N<}'3RԼm3Ĝ.V"0T&JM}'Fifog(~*iFOѻl^XhmYMz֡ jj)s1[q+gtx܌* ϗP͇ݵUK+<&pJD夨P [bx'- ^7+ E>Xiٮ9;"ӡ1VLDӐJLaO_ SI"l#PVCD@CH25-Y]8J|6xZÄg 15̠[B<d؅ak)fIFL. <ٔ3 zs K{ξk؛UA\+c08_Ț*QJSU.RptW%KƎC (e4IeE^e p%SgEiᖥ! yt}*toH+k"R)y#qM\Ra,8YTzn˞=][]`C1SR@Pb ժwѽ59y@ͼĐ21M@?#*TW+q~t$+ `Y58}+&p'PWxr4!s9yK?oܒdx R E}wݴ FRsV %wi1YPhJɌ\W^AsMIqncUi9tT* FZ 1Q\ru"Wh;! !Me@uBX&BT;]"<MKdR f ޭL##,SP3;)!-[RAbX%'rIo@Đf?3 RqRh \ʝ|ء՝F> endobj 23 0 obj << /Font << /F59 11 0 R /F8 12 0 R /F76 26 0 R /F75 27 0 R /F11 16 0 R /F1 28 0 R /F7 17 0 R /F24 6 0 R >> /ProcSet [ /PDF /Text ] >> endobj 31 0 obj << /Length 2014 /Filter /FlateDecode >> stream xڵr6дR3&C\Ӻ3qIQdJQ*(ymA}h@ |1y2KGEPQ:G*,FY**Fc?5,߽0V}c?wQhM~#_H;yL}`gȆ_ F#qˊN/s_kg~["AxpNnBM%߆ C(3S}딲q2vs 2w >K3DKFFdF%Z1Mgd!T>41$Y@]i8oz+ Dg&ȳ:O , >IWpsW,GV dBn\iyq񊒷)Gkn)J~2\b^?cFɶTvGH% BЊ2a" 3SLZqquClݴQHrvה-!ia@ne㉪ _5rH?E$wOt>5{f75`J9e/)4;t"̻o#E93,2*?yJY7fcw&Vvu"LTZPDccdE޻lWsn9BoL@t=5r*˾Dj^nE#T-)^2z=Pe6mI*`:u?l& M$6Ds&R[gjWe`j:xpII7L.*ˍiS3/mINXhK>oN*slB[:HK顽>/bȇ{/xmSu'Q,)kK1+vY- F |k"-O(MG}bOշNq+>3#레3Q( wm!wV^:M=0lavTGqgG!K{(ʝݘAѩptHT)Hv7=@}<)?ÂSV%7d-N$Ϭ<'0$ZA=BbkvN[uGCO`6dεc-F5s>ztɀkUgvVmRܓ&QƉ?Qs 4{H)z/|>&V> ;naT@.RU-H[K̺b;۪7=Y*g>+seӤlz6n }_7-βN}[]i\oy>mQJQ n{FBL٫{+;:(ϩ.3S8u{i2*2六pʡ̾-5+@-82y5C)L m]bmH f-mB:@~BW_"P8ŭXv9݆C"HJ@`BLٛɳF7 endstream endobj 30 0 obj << /Type /Page /Contents 31 0 R /Resources 29 0 R /MediaBox [0 0 595.276 841.89] /Parent 22 0 R >> endobj 29 0 obj << /Font << /F76 26 0 R /F8 12 0 R >> /ProcSet [ /PDF /Text ] >> endobj 34 0 obj << /Length 2035 /Filter /FlateDecode >> stream xr6$ݺdN:Y=ie[D:Zb{!әfX ~ti,aRgIF5aHN#E>ea[Zš`ZlKilxdX"ʁ7N9(푃Wdھ\dwG?%41F :r {Xg;C˖a;BTQv[^ӲAws\{D=A{ oaqX ko݄ю\P*o 5 9CcXvW KJw?hC+h6KXud\wMdV&Few3'sn(#ญww6P;CrBue>̓460ilb@cy^쏄O^X ^sG4aU#^HV=2.Q+\21EF tG ۲!r0,y 2Dgb>.Qij0nm@b,ԯWh\Z jSZȶj"Pcz*2kD_;w/a {)ep9X!s{pwYP`EJ кhm3ΝxNкpGCCS ˳G_>tb,P/\|9"3SF8yx`ebZ͎uk5r)hqǜ}V븍׮rl5gqj_xGd? 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00000 n 0000198028 00000 n 0000205073 00000 n 0000205300 00000 n 0000219789 00000 n 0000220095 00000 n 0000241288 00000 n 0000241853 00000 n 0000244884 00000 n 0000245112 00000 n 0000251136 00000 n 0000251432 00000 n 0000259293 00000 n 0000262778 00000 n 0000262853 00000 n 0000262906 00000 n trailer << /Size 141 /Root 139 0 R /Info 140 0 R /ID [<9C45B51E12B47543DC61F506A0252FE8> <9C45B51E12B47543DC61F506A0252FE8>] >> startxref 263129 %%EOF nloptr/inst/doc/nloptr.Rnw0000644000176200001440000003705612367224773015350 0ustar liggesusers\documentclass[a4paper]{article} \usepackage[round,authoryear,sort&compress]{natbib} \usepackage[english]{babel} \usepackage{graphicx} % \VignetteIndexEntry{Introduction to nloptr: an R interface to NLopt} % \VignetteKeyword{optimize} % \VignetteKeyword{interface} \SweaveOpts{keep.source=TRUE} \SweaveOpts{prefix.string = figs/plot, eps = FALSE, pdf = TRUE, tikz = FALSE} \title{Introduction to \texttt{nloptr}: an R interface to NLopt \thanks{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 \texttt{Sweave} (Leisch, 2002). 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.}} \author{Jelmer Ypma} \begin{document} \maketitle \nocite{Leisch2002} \DefineVerbatimEnvironment{Sinput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} <>= # 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)))) @ \begin{abstract} This document describes how to use \texttt{nloptr}, which is 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. \end{abstract} \nocite{NLopt:website} \section{Introduction} NLopt addresses general nonlinear optimization problems of the form: \begin{eqnarray*} &&\min_{x \in R^n} f(x) \\ &s.t.& g(x) \leq 0 \\ && h(x) = 0 \\ && x_L \leq x \leq x_U \end{eqnarray*} 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 can be specified in $g(\cdot)$, and equality constraints that can 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 avialable. Some of the information here has been taken from the NLopt website\footnote{\texttt{http://ab-initio.mit.edu/nlopt}}, where more details are available. All credit for implementing the C code for the different algorithms availalbe in NLopt should go to the respective authors. See the website\footnote{\texttt{http://ab-initio.mit.edu/wiki/index.php/Citing\_NLopt}} for information on how to cite NLopt and the algorithms you use. \section{Installation} This package is on CRAN and can be installed from within R using <>= install.packages("nloptr") @ You should now be able to load the R interface to NLopt and read the help. <>= library('nloptr') ?nloptr @ The most recent experimental version of \texttt{nloptr} can be installed from R-Forge using <>= install.packages("nloptr",repos="http://R-Forge.R-project.org") @ or from source using <>= install.packages("nloptr",type="source",repos="http://R-Forge.R-project.org") @ \section{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 \texttt{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) { return( 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2 ) } ## Gradient of Rosenbrock Banana function 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]) ) ) } @ We define initial values <>= # initial values x0 <- c( -1.2, 1 ) @ and then minimize the function using the \texttt{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 \citep{Nocedal:1980, LiuNocedal:1989}. The characters \texttt{LD} in the algorithm show that this algorithm looks for local minima (\texttt{L}) using a derivative-based (\texttt{D}) algorithm. Other algorithms look for global (\texttt{G}) minima, or they don't need derivatives (\texttt{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 ) @ 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] return( 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 ) @ This gives the same results as before. \section{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{eqnarray*} &&\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{eqnarray*} 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{eqnarray*} ( a_1 x_1 + b_1 )^3 - x_2 &\leq& 0 \\ ( a_2 x_1 + b_2 )^3 - x_2 &\leq& 0. \end{eqnarray*} First we define R functions to calculate the objective function and its gradient <>= # objective function eval_f0 <- function( x, a, b ){ return( sqrt(x[2]) ) } # gradient of objective function eval_grad_f0 <- function( x, a, b ){ return( c( 0, .5/sqrt(x[2]) ) ) } @ If needed, these can of course be calculated in the same function as before. Then we define the two constraints and the jacobian of the constraints <>= # constraint function eval_g0 <- function( x, a, b ) { return( (a*x[1] + b)^3 - 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 ) ) ) } @ Note that all of the functions above depend on additional parameters, \texttt{a} and \texttt{b}. We have to supply specific values for these when we invoke the optimization command. The constraint function \texttt{eval\_g0} returns a vector with in this case the same length as the vectors \texttt{a} and \texttt{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 ) print( res0 ) @ Here we supplied lower bounds for $x_2$ in \texttt{lb}. There are no upper bounds for both control variables, so we supply \texttt{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 \texttt{eval\_g\_ineq} and \texttt{eval\_jac\_g\_ineq}. Not all algorithms can handle inequality constraints, so we have to specifiy one that does, \texttt{NLOPT\_LD\_MMA} \citep{Svanberg:2002}. We also specify the option \texttt{print\_level} to obtain output during the optimization process. For the available \texttt{print\_level} values, see \texttt{?nloptr}. Setting the \texttt{check\_derivatives} option to \texttt{TRUE}, compares the gradients supplied by the user with a finite difference approximation in the initial point (\texttt{x0}). When this check is run, the option \texttt{check\_derivatives\_print} can be used to print all values of the derivative checker (\texttt{all} (default)), only those values that result in an error (\texttt{errors}) or no output (\texttt{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 \texttt{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, \texttt{a} and \texttt{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 \texttt{NLOPT\_LN\_COBYLA}, which is an algorithm that doesn't need gradient information \citep{Powell:1994, Powell: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 ) @ \section{Derivative checker} The derivative checker can be called when supplying a minimization problem to \texttt{nloptr}, using the options \texttt{check\_derivatives}, \texttt{check\_derivatives\_tol} and \texttt{check\_derivatives\_print}, but it can also be used separately. For example, define the function \texttt{g}, with vector outcome, and its gradient \texttt{g\_grad} <>= g <- function( x, a ) { return( 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 ) { return( 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 ) ) ) } @ \texttt{a} is some vector containing data. The gradient contains some errors in this case. By calling the function \texttt{check.derivatives} we can check the user-supplied analytic gradients with a finite difference approximation at a point \texttt{.x}. <>= res <- check.derivatives( .x=c(1,2), func=g, func_grad=g_grad, check_derivatives_print='all', a=c(.3, .8) ) @ The errors are shown on screen, where the option \texttt{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 @ Note that not all errors will be picked up by the derivative checker. For instance, if we run the check with \texttt{a = c(.5, .5)}, one of the errors is not flagged as an error. \section{Notes} The \texttt{.R} scripts in the \texttt{tests} directory contain more examples. For instance, \texttt{hs071.R} and \texttt{systemofeq.R} show how to solve problems with equality constraints. See also \texttt{http://ab-initio.mit.edu/wiki/index.php/NLopt\_Algorithms\#Augmented\_Lagrangian\_algorithm} for more details. Please let me know if you're missing any of the features that are implemented in NLopt. Sometimes the optimization procedure terminates with a message \texttt{maxtime was reached} without evaluating the objective function. Submitting the same problem again usually solves this problem. \bibliographystyle{plainnat} \bibliography{reflist} \appendix \section{Description of options} \label{sec:descoptions} <>= nloptr.print.options() @ \end{document} nloptr/configure.ac0000644000176200001440000001353612367224754014102 0ustar liggesusers## -*- mode: autoconf; autoconf-indentation: 4; -*- ## ## nloptr configure.ac ## ## nloptr -- R interface to NLopt ## ## Copyright (C) 2014 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(2.61) # Process this file with autoconf to produce a configure script. AC_INIT([nloptr], [1.0.1]) # We are using C++ AC_LANG(C++) AC_REQUIRE_CPP AC_PROG_CXX ## check for pkg-config AC_DEFUN([AC_PROG_PKGCONFIG], [AC_CHECK_PROG(PKGCONFIG,pkg-config,yes)]) AC_PROG_PKGCONFIG ## default to assuming no sufficient NLopt library has been found nlopt_good="no" nlopt_cflags="" nlopt_libs="" ## consider command-line options if given ## AC_ARG_WITH([nlopt-cflags], AC_HELP_STRING([--with-nlopt-cflags=CFLAGS], [Supply compiler flags such as the location of NLopt header files]), [nlopt_cflags=$withval], [nlopt_cflags=""]) AC_ARG_WITH([nlopt-libs], AC_HELP_STRING([--with-nlopt-libs=LIBS], [Supply the linker flags such as the location and name of NLopt libraries]), [nlopt_libs=$withval], [nlopt_libs=""]) ## also use pkg-config to check for NLopt ## if test x"${nlopt_libs}" == x""; then if test x"${PKGCONFIG}" == x"yes"; then ## check via pkg-config for hiredis if pkg-config --exists nlopt; then ## obtain cflags and obtain libs nlopt_cflags=$(pkg-config --cflags nlopt) nlopt_libs=$(pkg-config --libs nlopt) nlopt_version=$(pkg-config --modversion nlopt) nlopt_good="yes" case ${nlopt_version} in 1.*|2.0.*|2.1.*|2.2.*|2.3.*) AC_MSG_WARN([Only NLopt version 2.4.0 or greater can be used with nloptr.]) nlopt_good="no" ;; esac fi fi fi ## And make sure these flags are used for the test below. CPPFLAGS="${nlopt_cflags} ${CPPFLAGS}" CXXFLAGS="${nlopt_cflags} ${CXXFLAGS}" ## check for headers Debian has in libhiredis-dev AC_MSG_NOTICE([Now testing for NLopt header file.]) nlopt_header=nlopt.h AC_CHECK_HEADER([$nlopt_header], [nlopt_good="yes"], # may want to check for minimal version here too [nlopt_good="no"], []) ## in case neither of the two methods above worked, download NLopt and build it locally if test x"${nlopt_good}" = x"no"; then AC_MSG_NOTICE([Need to download and build NLopt]) ## define NLopt version NLOPT_VERSION=2.4.2 ## define NLopt file and download URL NLOPT_TGZ="nlopt-${NLOPT_VERSION}.tar.gz" NLOPT_URL="http://ab-initio.mit.edu/nlopt/${NLOPT_TGZ}" ## C Compiler options NLOPTR_CFLAGS= ## additional C Compiler options for linking NLOPTR_CLINKFLAGS= ## Libraries necessary to link with NLopt NLOPTR_LIBS="-lm $(pwd)/nlopt-${NLOPT_VERSION}/lib/libnlopt_cxx.a" ## Necessary Include dirs NLOPTR_INCL="-I$(pwd)/nlopt-${NLOPT_VERSION}/include" ## Set R_HOME, respecting an environment variable if set : ${R_HOME=$(R RHOME)} if test -z "${R_HOME}"; then AC_MSG_ERROR([Could not determine R_HOME.]) fi ## Get R compilers and flags NLOPT_CC=$("${R_HOME}/bin/R" CMD config CC) NLOPT_CFLAGS=$("${R_HOME}/bin/R" CMD config CFLAGS) NLOPT_CPP=$("${R_HOME}/bin/R" CMD config CPP) NLOPT_CPPFLAGS=$("${R_HOME}/bin/R" CMD config CPPFLAGS) NLOPT_CXX=$("${R_HOME}/bin/R" CMD config CXX) NLOPT_CXXFLAGS=$("${R_HOME}/bin/R" CMD config CXXFLAGS) NLOPT_CXXCPP=$("${R_HOME}/bin/R" CMD config CXXCPP) ## report values #echo "${NLOPT_CC} | ${NLOPT_CFLAGS} | ${NLOPT_CPPFLAGS} | ${NLOPT_CPPFLAGS} | ${NLOPT_CXX} | ${NLOPT_CXXFLAGS} | ${NLOPT_CXXCPP}" ## Download NLopt source code ## curl -O http://ab-initio.mit.edu/nlopt/nlopt-${NLOPT_VERSION}.tar.gz $("${R_HOME}/bin/Rscript" --vanilla -e "download.file(url='${NLOPT_URL}', destfile='${NLOPT_TGZ}')") ## Extract NLopt source code and remove .tar.gz ## tar -xzvf nlopt-${NLOPT_VERSION}.tar.gz $("${R_HOME}/bin/Rscript" --vanilla -e "untar(tarfile='${NLOPT_TGZ}')") $(rm -rf ${NLOPT_TGZ}) ## Compile NLopt source code and clean up ## --prefix="`pwd`", which is the directory we want to ## install in, after we changed our current directory AC_MSG_NOTICE([Starting to install library to $(pwd)/nlopt-${NLOPT_VERSION}]) $(cd nlopt-${NLOPT_VERSION}; \ ed -s isres/isres.c <<< $'H\n,s/sqrt(/sqrt((double) /g\nw'; \ ed -s util/qsort_r.c <<< $'H\n1i\nextern "C" {\n.\nw'; \ ed -s util/qsort_r.c <<< $'H\n$a\n}\n.\nw' ; \ ./configure --prefix="$(pwd)" --enable-shared --enable-static --without-octave \ --without-matlab --without-guile --without-python --with-cxx \ CC="${NLOPT_CC}" CFLAGS="${NLOPT_CFLAGS}" CPP="${NLOPT_CPP}" \ CPPFLAGS="${NLOPT_CPPFLAGS}" CXX="${NLOPT_CXX}" \ CXXFLAGS="${NLOPT_CXXFLAGS}" CXXCPP="${NLOPT_CXXCPP}" > /dev/null 2>&1; \ make > /dev/null 2>&1; \ make install > /dev/null 2>&1; \ ls | grep -v "^include$" | grep -v "^lib$" | xargs rm -rf; \ rm -rf .libs;) AC_MSG_NOTICE([Done installing library to $(pwd)/nlopt-${NLOPT_VERSION}]) ## Store compiler and linker flags nlopt_cflags="${NLOPTR_CFLAGS} ${NLOPTR_INCL}" nlopt_libs="${NLOPTR_CLINKFLAGS} ${NLOPTR_LIBS}" #echo "${NLOPTR_CFLAGS} | ${NLOPTR_INCL} | ${NLOPTR_CLINKFLAGS} | ${NLOPTR_LIBS}" else AC_MSG_NOTICE([Suitable NLopt library found.]) fi ## could add a test of building a three-liner here ## now use all these AC_SUBST([PKG_CFLAGS],["${PKG_CFLAGS} $nlopt_cflags"]) AC_SUBST([PKG_LIBS],["${PKG_LIBS} $nlopt_libs"]) AC_CONFIG_FILES([src/Makevars]) AC_OUTPUT nloptr/tests/0000755000176200001440000000000012367224755012747 5ustar liggesusersnloptr/tests/testthat/0000755000176200001440000000000012367224755014607 5ustar liggesusersnloptr/tests/testthat/test-banana-global.R0000644000176200001440000001136712367224755020375 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: test-banana-global.R # Author: Jelmer Ypma # Date: 8 August 2011 # # Example showing how to solve the Rosenbrock Banana function # using a global optimization algorithm. # # Changelog: # 27/10/2013: Changed example to use unit testing framework testthat. context("Banana Global") ## Rosenbrock Banana objective function eval_f <- function(x) { return( 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2 ) } eval_grad_f <- function(x) { return( c( -400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), 200 * (x[2] - x[1] * x[1])) ) } # initial values x0 <- c( -1.2, 1 ) # lower and upper bounds lb <- c( -3, -3 ) ub <- c( 3, 3 ) test_that("Test Rosenbrock Banana optimization with global optimizer NLOPT_GD_MLSL.", { # Define optimizer options. local_opts <- list( "algorithm" = "NLOPT_LD_LBFGS", "xtol_rel" = 1e-4 ) opts <- list( "algorithm" = "NLOPT_GD_MLSL", "maxeval" = 10000, "population" = 4, "local_opts" = local_opts ) # Solve Rosenbrock Banana function. res <- nloptr( x0 = x0, lb = lb, ub = ub, eval_f = eval_f, eval_grad_f = eval_grad_f, opts = opts ) # Check results. expect_that( res$objective, equals( 0.0 ) ) expect_that( res$solution, equals( c( 1.0, 1.0 ) ) ) } ) test_that("Test Rosenbrock Banana optimization with global optimizer NLOPT_GN_ISRES.", { # Define optimizer options. # For unit testing we want to set the random seed for replicability. opts <- list( "algorithm" = "NLOPT_GN_ISRES", "maxeval" = 10000, "population" = 100, "ranseed" = 2718 ) # Solve Rosenbrock Banana function. res <- nloptr( x0 = x0, lb = lb, ub = ub, eval_f = eval_f, opts = opts ) # Check results. expect_that( res$objective, equals( 0.0, tolerance=1e-4 ) ) expect_that( res$solution, equals( c( 1.0, 1.0 ), tolerance=1e-2 ) ) } ) test_that("Test Rosenbrock Banana optimization with global optimizer NLOPT_GN_CRS2_LM with random seed defined.", { # Define optimizer options. # For unit testing we want to set the random seed for replicability. opts <- list( "algorithm" = "NLOPT_GN_CRS2_LM", "maxeval" = 10000, "population" = 100, "ranseed" = 2718 ) # Solve Rosenbrock Banana function. res1 <- nloptr( x0 = x0, lb = lb, ub = ub, eval_f = eval_f, opts = opts ) # Define optimizer options. # this optimization uses a different seed for the # random number generator and gives a different result opts <- list( "algorithm" = "NLOPT_GN_CRS2_LM", "maxeval" = 10000, "population" = 100, "ranseed" = 3141 ) # Solve Rosenbrock Banana function. res2 <- nloptr( x0 = x0, lb = lb, ub = ub, eval_f = eval_f, opts = opts ) # Define optimizer options. # this optimization uses the same seed for the random # number generator and gives the same results as res2 opts <- list( "algorithm" = "NLOPT_GN_CRS2_LM", "maxeval" = 10000, "population" = 100, "ranseed" = 3141 ) # Solve Rosenbrock Banana function. res3 <- nloptr( x0 = x0, lb = lb, ub = ub, eval_f = eval_f, opts = opts ) # Check results. expect_that( res1$objective, equals( 0.0, tolerance=1e-4 ) ) expect_that( res1$solution, equals( c( 1.0, 1.0 ), tolerance=1e-2 ) ) expect_that( res2$objective, equals( 0.0, tolerance=1e-4 ) ) expect_that( res2$solution, equals( c( 1.0, 1.0 ), tolerance=1e-2 ) ) expect_that( res3$objective, equals( 0.0, tolerance=1e-4 ) ) expect_that( res3$solution, equals( c( 1.0, 1.0 ), tolerance=1e-2 ) ) # Expect that the results are different for res1 and res2. expect_that( res1$objective == res2$objective, is_false() ) expect_that( all( res1$solution == res2$solution ), is_false() ) # Expect that the results are identical for res2 and res3. expect_that( res2$objective, is_identical_to( res3$objective ) ) expect_that( res2$solution, is_identical_to( res3$solution ) ) } ) nloptr/tests/testthat/test-simple.R0000644000176200001440000000555012367224755017205 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: simple.R # Author: Jelmer Ypma # Date: 20 June 2010 # # Example showing how to solve a simple constrained problem. # # min x^2 # s.t. x >= 5 # # re-formulate constraint to be of form g(x) <= 0 # 5 - x <= 0 # we could use a bound constraint as well here # # CHANGELOG: # 05/05/2014: Changed example to use unit testing framework testthat. context("Simple contstrained problem.") test_that( "Test simple constrained optimization problem with gradient information." , { # Objective function. eval_f <- function(x) { return( x^2 ) } # Gradient of objective function. eval_grad_f <- function(x) { return( 2*x ) } # Inequality constraint function. eval_g_ineq <- function( x ) { return( 5 - x ) } # Jacobian of constraint. eval_jac_g_ineq <- function( x ) { return( -1 ) } # Optimal solution. solution.opt <- 5 # Solve using NLOPT_LD_MMA with gradient information supplied in separate function res <- nloptr( x0 = 1, eval_f = eval_f, eval_grad_f = eval_grad_f, eval_g_ineq = eval_g_ineq, eval_jac_g_ineq = eval_jac_g_ineq, opts = list("algorithm"="NLOPT_LD_MMA", "xtol_rel" = 1e-4) ) # Run some checks on the optimal solution. expect_that( res$solution, equals( solution.opt ) ) # Check whether constraints are violated (up to specified tolerance). expect_that( eval_g_ineq( res$solution ) <= res$options$tol_constraints_ineq, is_true() ) } ) test_that( "Test simple constrained optimization problem without gradient information." , { # Objective function. eval_f <- function(x) { return( x^2 ) } # Inequality constraint function. eval_g_ineq <- function( x ) { return( 5 - x ) } # Optimal solution. solution.opt <- 5 # Solve using NLOPT_LN_COBYLA without gradient information res <- nloptr( x0 = 1, eval_f = eval_f, eval_g_ineq = eval_g_ineq, opts = list( "algorithm" = "NLOPT_LN_COBYLA", "xtol_rel" = 1e-6, "tol_constraints_ineq" = 1e-6 ) ) # Run some checks on the optimal solution. expect_that( res$solution, equals( solution.opt, tolerance = 1e-6 ) ) # Check whether constraints are violated (up to specified tolerance). expect_that( eval_g_ineq( res$solution ) <= res$options$tol_constraints_ineq, is_true() ) } ) nloptr/tests/testthat/test-parameters.R0000644000176200001440000000314512367224755020055 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: parameters.R # Author: Jelmer Ypma # Date: 17 August 2010 # # Example shows how we can have an objective function # depend on parameters or data. The objective function # is a simple polynomial. # # CHANGELOG: # 05/05/2014: Changed example to use unit testing framework testthat. context("Simple polynomial with additional data.") test_that( "Test simple polyonmial where parameters are supplied as additional data.", { # Objective function and gradient in terms of parameters. eval_f <- function(x, params) { return( params[1]*x^2 + params[2]*x + params[3] ) } eval_grad_f <- function(x, params) { return( 2*params[1]*x + params[2] ) } # Define parameters that we want to use. params <- c(1,2,3) # Define initial value of the optimzation problem. x0 <- 0 # solve using nloptr adding params as an additional parameter res <- nloptr( x0 = x0, eval_f = eval_f, eval_grad_f = eval_grad_f, opts = list("algorithm"="NLOPT_LD_MMA", "xtol_rel" = 1e-6), params = params ) # Solve using algebra # Minimize f(x) = ax^2 + bx + c. # Optimal value for control is -b/(2a). expect_that( res$solution, equals( -params[2]/(2*params[1]), tolerance = 1e-7 ) ) # With value of the objective function f(-b/(2a)). expect_that( res$objective, equals( eval_f( -params[2]/(2*params[1]), params ) ) ) } ) nloptr/tests/testthat/test-hs023.R0000644000176200001440000000540412367224755016551 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: hs023.R # Author: Jelmer Ypma # Date: 16 August 2010 # # Example problem, number 23 from the Hock-Schittkowsky test suite.. # # \min_{x} x1^2 + x2^2 # s.t. # x1 + x2 >= 1 # x1^2 + x2^2 >= 1 # 9*x1^2 + x2^2 >= 9 # x1^2 - x2 >= 0 # x2^2 - x1 >= 0 # # with bounds on the variables # -50 <= x1, x2 <= 50 # # we re-write the inequalities as # 1 - x1 - x2 <= 0 # 1 - x1^2 - x2^2 <= 0 # 9 - 9*x1^2 - x2^2 <= 0 # x2 - x1^2 <= 0 # x1 - x2^2 <= 0 # # the initial value is # x0 = (3, 1) # # Optimal solution = (1, 1) # # CHANGELOG: # 05/05/2014: Changed example to use unit testing framework testthat. context("HS023") test_that( "Test HS023.", { # # f(x) = x1^2 + x2^2 # eval_f <- function( x ) { return( list( "objective" = x[1]^2 + x[2]^2, "gradient" = c( 2*x[1], 2*x[2] ) ) ) } # Inequality constraints. eval_g_ineq <- function( x ) { constr <- c( 1 - x[1] - x[2], 1 - x[1]^2 - x[2]^2, 9 - 9*x[1]^2 - x[2]^2, x[2] - x[1]^2, x[1] - x[2]^2 ) grad <- rbind( c( -1, -1 ), c( -2*x[1], -2*x[2] ), c( -18*x[1], -2*x[2] ), c( -2*x[1], 1 ), c( 1, -2*x[2] ) ) return( list( "constraints"=constr, "jacobian"=grad ) ) } # Initial values. x0 <- c( 3, 1 ) # Lower and upper bounds of control. lb <- c( -50, -50 ) ub <- c( 50, 50 ) # Optimal solution. solution.opt <- c( 1, 1 ) # Solve with MMA. opts <- list( "algorithm" = "NLOPT_LD_MMA", "xtol_rel" = 1.0e-7, "tol_constraints_ineq" = rep( 1.0e-6, 5 ), "print_level" = 0 ) res <- nloptr( x0 = x0, eval_f = eval_f, lb = lb, ub = ub, eval_g_ineq = eval_g_ineq, opts = opts ) # Run some checks on the optimal solution. expect_that( res$solution, equals( solution.opt, tolerance = 1e-7 ) ) expect_that( all( res$solution >= lb ), is_true() ) expect_that( all( res$solution <= ub ), is_true() ) # Check whether constraints are violated (up to specified tolerance). expect_that( all( eval_g_ineq( res$solution )$constr <= res$options$tol_constraints_ineq ), is_true() ) } ) nloptr/tests/testthat/test-example.R0000644000176200001440000000751412367224755017351 0ustar liggesusers# Copyright (C) 2010-14 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: test-example.R # Author: Jelmer Ypma # Date: 10 June 2010 # # 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: # 03/05/2014: Changed example to use unit testing framework testthat. context("Example-NLoptTutorial") # 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 ) # Define optimal solution. solution.opt <- c( 1/3, 8/27 ) test_that( "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_that( res0$solution, equals( solution.opt ) ) } ) test_that( "Test NLopt tutorial example with NLOPT_LN_COBYLA with gradient information.", { # Solve using NLOPT_LN_COBYLA without gradient information # A tighter convergence tolerance is used here (1e-6), to ensure # that the final solution is equal to the optimal solution (within some tolerance). res1 <- nloptr( x0 = c( 1.234, 5.678 ), eval_f = eval_f0, lb = c( -Inf, 0 ), ub = c( Inf, Inf ), eval_g_ineq = eval_g0, opts = list("xtol_rel" = 1e-6, "algorithm" = "NLOPT_LN_COBYLA"), a = a, b = b ) expect_that( res1$solution, equals( solution.opt ) ) } ) test_that( "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_that( res2$solution, equals( solution.opt ) ) } ) nloptr/tests/testthat/options.R0000644000176200001440000000060412367224755016425 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: test_options.R # Author: Jelmer Ypma # Date: 7 August 2011 # # Test printing of options. library('nloptr') opts <- list( "algorithm" = "NLOPT_LD_LBFGS", "xtol_rel" = 1.0e-8, "print_level" = 1 ) nloptr.print.options( opts ) nloptr/tests/testthat/test-systemofeq.R0000644000176200001440000000727612367224755020122 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: systemofeq.R # Author: Jelmer Ypma # Date: 20 June 2010 # # 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: # 16/06/2011: added NLOPT_LD_SLSQP # 05/05/2014: Changed example to use unit testing framework testthat. context("System of equations.") test_that( "Solve system of equations using NLOPT_LD_MMA with local optimizer NLOPT_LD_MMA.", { # Objective function. eval_f0 <- function( x, params ) { return( 1 ) } # Gradient of objective function. eval_grad_f0 <- function( x, params ) { return( 0 ) } # Equality constraint function. eval_g0_eq <- function( x, params ) { return( params[1]*x^2 + params[2]*x + params[3] ) } # Jacobian of constraint. eval_jac_g0_eq <- function( x, params ) { return( 2*params[1]*x + params[2] ) } # Define vector with addiitonal data. params <- c(1, 1, -1) # Define optimal solution. solution.opt <- -1.61803398875 # # Solve using NLOPT_LD_MMA with local optimizer NLOPT_LD_MMA. # 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_that( res$solution, equals( solution.opt ) ) # Check whether constraints are violated (up to specified tolerance). expect_that( eval_g0_eq( res$solution, params = params ), equals( 0, tolerance = res$options$tol_constraints_eq ) ) } ) test_that( "Solve system of equations using NLOPT_LD_SLSQP.", { # Objective function. eval_f0 <- function( x, params ) { return( 1 ) } # Gradient of objective function. eval_grad_f0 <- function( x, params ) { return( 0 ) } # Equality constraint function. eval_g0_eq <- function( x, params ) { return( params[1]*x^2 + params[2]*x + params[3] ) } # Jacobian of constraint. eval_jac_g0_eq <- function( x, params ) { return( 2*params[1]*x + params[2] ) } # Define vector with addiitonal data. params <- c(1, 1, -1) # Define optimal solution. solution.opt <- -1.61803398875 # # Solve using NLOPT_LD_SLSQP. # opts <- list( "algorithm" = "NLOPT_LD_SLSQP", "xtol_rel" = 1.0e-6 ) res <- nloptr( x0 = -5, eval_f = eval_f0, eval_grad_f = eval_grad_f0, eval_g_eq = eval_g0_eq, eval_jac_g_eq = eval_jac_g0_eq, opts = opts, params = params ) # Run some checks on the optimal solution. expect_that( res$solution, equals( solution.opt ) ) # Check whether constraints are violated (up to specified tolerance). expect_that( eval_g0_eq( res$solution, params = params ), equals( 0, tolerance = res$options$tol_constraints_eq ) ) } ) nloptr/tests/testthat/test-banana.R0000644000176200001440000000456212367224755017136 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: test-banana.R # Author: Jelmer Ypma # Date: 10 June 2010 # # Example showing how to solve the Rosenbrock Banana function. # # Changelog: # 27/10/2013: Changed example to use unit testing framework testthat. context("Banana") test_that("Test Rosenbrock Banana optimization with objective and gradient in separate functions.", { # initial values x0 <- c( -1.2, 1 ) opts <- list( "algorithm" = "NLOPT_LD_LBFGS", "xtol_rel" = 1.0e-8, "print_level" = 0 ) ## Rosenbrock Banana function and gradient in separate functions eval_f <- function(x) { return( 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2 ) } eval_grad_f <- function(x) { return( c( -400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), 200 * (x[2] - x[1] * x[1])) ) } # Solve Rosenbrock Banana function. res <- nloptr( x0 = x0, eval_f = eval_f, eval_grad_f = eval_grad_f, opts = opts ) # Check results. expect_that( res$objective, equals( 0.0 ) ) expect_that( res$solution, equals( c( 1.0, 1.0 ) ) ) } ) test_that("Test Rosenbrock Banana optimization with objective and gradient in the same function.", { # initial values x0 <- c( -1.2, 1 ) opts <- list( "algorithm" = "NLOPT_LD_LBFGS", "xtol_rel" = 1.0e-8, "print_level" = 0 ) ## Rosenbrock Banana function and gradient in one function # this can be used to economize on calculations eval_f_list <- function(x) { return( list( "objective" = 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2, "gradient" = c( -400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), 200 * (x[2] - x[1] * x[1])) ) ) } # Solve Rosenbrock Banana function. using an objective function that # returns a list with the objective value and its gradient res <- nloptr( x0 = x0, eval_f = eval_f_list, opts = opts ) # Check results. expect_that( res$objective, equals( 0.0 ) ) expect_that( res$solution, equals( c( 1.0, 1.0 ) ) ) } ) nloptr/tests/testthat/test-hs071.R0000644000176200001440000000656212367224755016562 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: hs071.R # Author: Jelmer Ypma # Date: 10 June 2010 # # 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: # 05/05/2014: Changed example to use unit testing framework testthat. context("HS071") test_that( "Test HS071.", { # # f(x) = x1*x4*(x1 + x2 + x3) + x3 # eval_f <- function( x ) { return( 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]) ) ) ) } # 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] ) return( 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] ) return( 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_that( res$solution, equals( solution.opt, tolerance = 1e-6 ) ) expect_that( all( res$solution >= lb ), is_true() ) expect_that( all( res$solution <= ub ), is_true() ) # Check whether constraints are violated (up to specified tolerance). expect_that( eval_g_ineq( res$solution )$constr <= res$options$tol_constraints_ineq, is_true() ) expect_that( eval_g_eq( res$solution )$constr, equals( 0, tolerance = res$options$tol_constraints_eq ) ) } ) nloptr/tests/testthat/test-derivative-checker.R0000644000176200001440000000540712367224755021461 0ustar liggesusers# Copyright (C) 201 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: test-derivative-checker.R # Author: Jelmer Ypma # Date: 24 July 2010 # # Example showing results of the derivative checker. # # Changelog: # 27/10/2013: Changed example to use unit testing framework testthat. context("Derivative checker") test_that("Test derivative checker.", { # Define objective function. f <- function( x, a ) { return( sum( ( x - a )^2 ) ) } # Define gradient function without errors. f_grad <- function( x, a ) { return( 2*( x - a ) ) } res <- check.derivatives( .x=1:10, func=f, func_grad=f_grad, check_derivatives_print='none', a=runif(10) ) expect_that( sum( res$flag_derivative_warning ), equals( 0 ) ) # res <- check.derivatives( .x=1:10, func=f, func_grad=f_grad, check_derivatives_print='errors', a=runif(10) ) # expect_that( sum( res$flag_derivative_warning ), equals( 0 ) ) # # res <- check.derivatives( .x=1:10, func=f, func_grad=f_grad, check_derivatives_print='all', a=runif(10) ) # expect_that( sum( res$flag_derivative_warning ), equals( 0 ) ) # Define gradient function with 1 error. f_grad <- function( x, a ) { return( 2*( x - a ) + c(0,.1,rep(0,8)) ) } res <- check.derivatives( .x=1:10, func=f, func_grad=f_grad, check_derivatives_print='none', a=runif(10) ) expect_that( sum( res$flag_derivative_warning ), equals( 1 ) ) #res <- check.derivatives( .x=1:10, func=f, func_grad=f_grad, check_derivatives_print='errors', a=runif(10) ) #expect_that( sum( res$flag_derivative_warning ), equals( 1 ) ) # #res <- check.derivatives( .x=1:10, func=f, func_grad=f_grad, check_derivatives_print='all', a=runif(10) ) #expect_that( sum( res$flag_derivative_warning ), equals( 1 ) ) # Define objective function. g <- function( x, a ) { return( c( sum(x-a), sum( (x-a)^2 ) ) ) } # Define gradient function with 2 errors. g_grad <- function( x, a ) { return( rbind( rep(1,length(x)) + c(0,.01,rep(0,8)), 2*(x-a) + c(0,.1,rep(0,8)) ) ) } res <- check.derivatives( .x=1:10, func=g, func_grad=g_grad, check_derivatives_print='none', a=runif(10) ) expect_that( sum( res$flag_derivative_warning ), equals( 2 ) ) # res <- check.derivatives( .x=1:10, func=g, func_grad=g_grad, check_derivatives_print='errors', a=runif(10) ) # expect_that( sum( res$flag_derivative_warning ), equals( 2 ) ) # # res <- check.derivatives( .x=1:10, func=g, func_grad=g_grad, check_derivatives_print='all', a=runif(10) ) # expect_that( sum( res$flag_derivative_warning ), equals( 2 ) ) } ) nloptr/tests/test-all.R0000644000176200001440000000023212367224755014614 0ustar liggesusersif(require("testthat", quietly = TRUE)) { test_check("nloptr") } else { print( "package 'testthat' not available, cannot run unit tests" ) } nloptr/src/0000755000176200001440000000000012367224773012374 5ustar liggesusersnloptr/src/Makevars.in0000644000176200001440000001216212367224755014477 0ustar liggesusers ## We now use configure to find where NLopt is installed. ## ## If it is not found, it is downloaded and installed from source -- but such ## a build scheme is not permitted within Debian, or on Launchpad, or ... so ## the preference is use a supplied version of NLopt PKG_CFLAGS=@PKG_CFLAGS@ PKG_LIBS=@PKG_LIBS@ ## Old Makevars code below # Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: Makevars.in # Author: Jelmer Ypma # Date: 10 June 2010 # # 16-01-2011: Changed --disable-shared to --enable-shared to compile with -fPIC # 16-06-2011: Updated version number # 09-07-2011: Download and untar NLopt code using Rscript # 01-09-2011: Added check on empty SRCDIR # Added CC, CFLAGS, etc. to NLopt ./configure # 09-09-2011: Changed CURDIR to PWD which is not supported on Solaris Make # 21-10-2011: Changed ${PWD} to $(shell pwd) which is not supported on Solaris Make # 24-10-2011: Changed $(shell pwd) to `pwd` which is supported on Solaris Make # 24-10-2011: Removed SRCDIR macro, using `pwd` when needed instead # 28-10-2011: Changed shell to `` in downloading and extracting code # 18-11-2011: Changed CRLF and CR line endings to LF # 21-02-2013: Changed NLOPT_VERSION to 2.3 # Included --with-cxx option in configure to allow for StoGo algorithm. # Linking to libnlopt_cxx.a instead of libnlopt.a # 08-07-2013: Changed CFLAGS to NLOPT_CFLAGS and similarly for CC, CPP, CXX, # CXXFLAGS, and CXXCPP to prevent overriding user customizations. # For clarity some of the other macros are now prefixed with NLOPTR # instead of NLOPT. # 08-07-2013: Added --vanilla flag to Rscript. This solves problems if someone sets # a different home directory with setwd in Rprofile. # 08-07-2013: Added `pwd` to NLOPTR_LIBS and NLOPTR_INCL. # 05-11-2013: Changed NLOPT_VERSION to 2.4 # 07-11-2013: Removed -lstdc++ from linker statement. A file dummy.cpp (with C++ extension) # is added to the source directory to ensure linking with C++. Thanks to # Brian Ripley for bringing this up. # 12-11-2013: Replace 'sqrt(' by 'sqrt((double) ' in isres/isres/c in NLopt. This cast # is not implemented in NLopt, but causes compilation errors on some systems. # 19-11-2013: Wrap code in util/qsort_r.c in NLopt in extern "C" as requested by Brian # Ripley to fix compilation on Solaris. # 07-07-2014: Changed NLOPT_VERSION to 2.4.2 # # define NLopt version # NLOPT_VERSION = 2.4.2 # # C Compiler options # NLOPTR_CFLAGS = # # additional C Compiler options for linking # NLOPTR_CLINKFLAGS = # # Libraries necessary to link with NLopt # NLOPTR_LIBS = -lm `pwd`/nlopt-${NLOPT_VERSION}/lib/libnlopt_cxx.a # # Necessary Include dirs # NLOPTR_INCL = -I`pwd`/nlopt-${NLOPT_VERSION}/include # # Get R compilers and flags # NLOPT_CC=`"${R_HOME}/bin/R" CMD config CC` # NLOPT_CFLAGS=`"${R_HOME}/bin/R" CMD config CFLAGS` # NLOPT_CPP=`"${R_HOME}/bin/R" CMD config CPP` # NLOPT_CPPFLAGS=`"${R_HOME}/bin/R" CMD config CPPFLAGS` # NLOPT_CXX=`"${R_HOME}/bin/R" CMD config CXX` # NLOPT_CXXFLAGS=`"${R_HOME}/bin/R" CMD config CXXFLAGS` # NLOPT_CXXCPP=`"${R_HOME}/bin/R" CMD config CXXCPP` # # Define objects for R to build # OBJECTS = nloptr.o # # Convert to R macros # PKG_LIBS=${NLOPTR_CLINKFLAGS} ${NLOPTR_LIBS} # PKG_CFLAGS=${NLOPTR_CFLAGS} ${NLOPTR_INCL} # .PHONY: all # all: $(SHLIB) # $(SHLIB): nlopt-${NLOPT_VERSION}/lib/libnlopt_cxx.a ${OBJECTS} # nloptr.o: nlopt-${NLOPT_VERSION}/include/nlopt.h # # Compile NLopt source code and clean up # # --prefix="`pwd`", which is the directory we want to # # install in, after we changed our current directory # nlopt-${NLOPT_VERSION}/include/nlopt.h nlopt-${NLOPT_VERSION}/lib/libnlopt_cxx.a: nlopt-${NLOPT_VERSION}/configure # echo "Installing library to: `pwd`/nlopt-${NLOPT_VERSION}" # cd nlopt-${NLOPT_VERSION}; \ # ed -s isres/isres.c <<< $$'H\n,s/sqrt(/sqrt((double) /g\nw'; \ # ed -s util/qsort_r.c <<< $$'H\n1i\nextern "C" {\n.\nw'; \ # ed -s util/qsort_r.c <<< $$'H\n$$a\n}\n.\nw'; \ # ./configure --prefix="`pwd`" --enable-shared --enable-static --without-octave --without-matlab --without-guile --without-python --with-cxx CC="${NLOPT_CC}" CFLAGS="${NLOPT_CFLAGS}" CPP="${NLOPT_CPP}" CPPFLAGS="${NLOPT_CPPFLAGS}" CXX="${NLOPT_CXX}" CXXFLAGS="${NLOPT_CXXFLAGS}" CXXCPP="${NLOPT_CXXCPP}"; \ # make; \ # make install; \ # ls | grep -v ^include$$ | grep -v ^lib$$ | xargs rm -rf; \ # rm -rf .libs; # # Extract NLopt source code and remove .tar.gz # # tar -xzvf nlopt-${NLOPT_VERSION}.tar.gz # nlopt-${NLOPT_VERSION}/configure: nlopt-${NLOPT_VERSION}.tar.gz # `"${R_HOME}/bin/Rscript" --vanilla -e "untar(tarfile='nlopt-${NLOPT_VERSION}.tar.gz')"` # rm -rf nlopt-${NLOPT_VERSION}.tar.gz # # Download NLopt source code # # curl -O http://ab-initio.mit.edu/nlopt/nlopt-${NLOPT_VERSION}.tar.gz # nlopt-${NLOPT_VERSION}.tar.gz: # `"${R_HOME}/bin/Rscript" --vanilla -e "download.file(url='http://ab-initio.mit.edu/nlopt/nlopt-${NLOPT_VERSION}.tar.gz', destfile='nlopt-${NLOPT_VERSION}.tar.gz')"` # clean: # rm -rf *.so # rm -rf *.o # rm -rf nlopt-${NLOPT_VERSION} nloptr/src/dummy.cpp0000644000176200001440000000000012367225003014204 0ustar liggesusersnloptr/src/Makevars.win0000644000176200001440000000230512367224755014664 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: Makevars.win # Author: Jelmer Ypma # Date: 18 August 2010 # # 09 June 2011: Windows support added thanks to Stefan Theussl and Uwe Ligges. # NLOPT_HOME is the directory where a working installation of # NLopt is located (within subdirectories NLOPT_VERSION/R_ARCH) # 18 November 2011: Removed NLOPT_VERSION macro and adopted some other changes # proposed by Brian Ripley to make nloptr work with his new toolchain. # NLopt should now be located in NLOPT_HOME/R_ARCH (i.e. without # version number) # 19 February 2013: NLopt is compiled with --with-cxx option, in order to include # the StoGo algorithm. This means that we now need to link to # with -lnlopt_cxx and also link to the c++ library, -lstdc++. # 7 November 2013: Changed PKG_CPPFLAGS to PKG_CFLAGS. # 2 May 2014: Added quotes around include paths to allow for spaces in NLOPT_HOME. # C Compiler options PKG_CFLAGS = -I"$(NLOPT_HOME)$(R_ARCH)/include" PKG_LIBS = -L"$(NLOPT_HOME)$(R_ARCH)/lib" -lnlopt_cxx nloptr/src/nloptr.c0000644000176200001440000010530112367225003014041 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. * * 13/01/2011: added print_level option * 24/07/2011: added checks on return value when setting equality constraints etc. * 05/11/2013: Moved declaration of ineq_constr_data and eq_constr_data outside if-statement to solve segfault on Ubuntu. */ // 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 "nlopt.h" #include #include // Rdefines.h is somewhat more higher level then Rinternal.h, and is preferred if the code might be shared with S at any stage. // #include /* * Extracts element with name 'str' from R object 'list' * and returns that element. */ SEXP getListElement (SEXP list, char *str) { SEXP elmt = R_NilValue, names = getAttrib(list, R_NamesSymbol); int i; for (i = 0; i < length(list); i++) { if(strcmp(CHAR(STRING_ELT(names, i)), str) == 0) { elmt = VECTOR_ELT(list, i); break; } } return elmt; } // convert string to nlopt_alogirthm nlopt_algorithm getAlgorithmCode( const char *algorithm_str ) { nlopt_algorithm algorithm; 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_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 { // unknown algorithm code Rprintf("Error: unknown algorithm %s.\n", algorithm_str); algorithm = NLOPT_NUM_ALGORITHMS; // Not an algorithm, so this should result in a runtime error. } return algorithm; } /* * Define structure that contains data to pass to the objective function */ typedef struct { SEXP R_eval_f; SEXP R_environment; int 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) of the objective function // Check for user interruption from R R_CheckUserInterrupt(); // declare counter unsigned i; 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: %d\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 (i=1;iR_eval_f,rargs)); PROTECT(result = eval(Rcall,d->R_environment)); // recode the return value from SEXP to double double obj_value; if ( isNumeric( result ) ) { // objective value is only element of result obj_value = REAL(result)[0]; } else { // objective value should be parsed from the list of return values SEXP R_obj_value; PROTECT( R_obj_value = getListElement( result, "objective" ) ); // recode the return value from SEXP to double obj_value = REAL( R_obj_value )[0]; UNPROTECT( 1 ); } // print objective value if ( d->print_level >= 1 ) { Rprintf( "\tf(x) = %f\n", obj_value ); } // gradient if (grad) { // result needs to be a list in this case SEXP R_gradient; PROTECT( R_gradient = getListElement( result, "gradient" ) ); // recode the return value from SEXP to double for (i=0;iR_eval_g, rargs_x ) ); PROTECT( result = 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 // recode the return value from SEXP to double*, by looping over constraints for (i=0;iprint_level >= 2 ) { if ( m == 1 ) { Rprintf( "\tg(x) = %f\n", constraints[ 0 ] ); } else { Rprintf( "\tg(x) = ( %f", constraints[ 0 ] ); for (i=1;iR_eval_g, rargs_x ) ); PROTECT( result = 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 // recode the return value from SEXP to double*, by looping over constraints for (i=0;iprint_level >= 2 ) { if ( m == 1 ) { Rprintf( "\th(x) = %f\n", constraints[ 0 ] ); } else { Rprintf( "\th(x) = ( %f", constraints[ 0 ] ); for (i=1;i= stopval for maximizing PROTECT( R_opts_stopval = getListElement( R_options, "stopval" ) ); double stopval = REAL( R_opts_stopval )[0]; 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( R_opts_ftol_rel = getListElement( R_options, "ftol_rel" ) ); double ftol_rel = REAL( R_opts_ftol_rel )[0]; 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( R_opts_ftol_abs = getListElement( R_options, "ftol_abs" ) ); double ftol_abs = REAL( R_opts_ftol_abs )[0]; 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( R_opts_xtol_rel = getListElement( R_options, "xtol_rel" ) ); double xtol_rel = REAL( R_opts_xtol_rel )[0]; 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( R_opts_xtol_abs = getListElement( R_options, "xtol_abs" ) ); double xtol_abs[ num_controls ]; int i; for (i=0;i 0. // by default a random seed is generated from system time. if ( ranseed > 0 ) { nlopt_srand(ranseed); } UNPROTECT( 11 ); return opts; } SEXP convertStatusToMessage( nlopt_result status ) { // convert message to an R object SEXP R_status_message; PROTECT(R_status_message = 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; 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.")); default: SET_STRING_ELT(R_status_message, 0, mkChar("Return status not recognized.")); } UNPROTECT( 1 ); return R_status_message; } // // Constrained minimization // SEXP NLoptR_Optimize( SEXP args ) { // declare counter unsigned i; // 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( R_init_values = getListElement( args, "x0" ) ); // number of control variables unsigned num_controls = length( R_init_values ); // set initial values of the controls double x0[ num_controls ]; for (i=0;i 0 ) { // get tolerances from R_options double tol_constraints_ineq[ num_constraints_ineq ]; SEXP R_tol_constraints_ineq; PROTECT( R_tol_constraints_ineq = getListElement( R_options, "tol_constraints_ineq" ) ); for (i=0;i 0 ) { // get tolerances from R_options double tol_constraints_eq[ num_constraints_eq ]; SEXP R_tol_constraints_eq; PROTECT( R_tol_constraints_eq = getListElement( R_options, "tol_constraints_eq" ) ); for (i=0;i= 0 to hin <= 0 ! if (is.null(hinjac)) { hinjac <- function(x) nl.jacobian(x, hin) } else { .hinjac <- match.fun(hinjac) hinjac <- function(x) (-1) * .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) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } nloptr/R/check.derivatives.R0000644000176200001440000001101612367224754015530 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # 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: # 27/10/2013: Added relative_error and flag_derivative_warning to output list. # 05/05/2014: Replaced cat by message, so messages can now be suppressed by suppressMessages. 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( paste( "Value '", check_derivatives_print, "' for check_derivatives_print is unknown; use 'all' (default), 'errors', or 'none'.", sep='' ) ) 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( 1:nrow(analytic_grad), times=ncol(analytic_grad) ), width=1 + sum( nrow(analytic_grad) > 10^(1:10) ) ), format( rep( 1:ncol(analytic_grad), each=nrow(analytic_grad) ), width=1 + sum( ncol(analytic_grad) > 10^(1:10) ) ), sep=', ' ) } else { indices <- format( 1:length(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", paste( ifelse( flag_derivative_warning, "*"," "), " ", func_grad_name, "[ ", indices, " ] = ", format(analytic_grad, scientific=TRUE), " ~ ", format(finite_diff_grad, scientific=TRUE), " [", format( relative_error, scientific=TRUE), "]", sep='', collapse="\n" ), "\n\n" ) } else if ( check_derivatives_print == 'errors' ) { if ( sum( flag_derivative_warning ) > 0 ) { message( "\n", paste( 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), "]", sep='', collapse="\n" ), "\n\n" ) } } else if ( check_derivatives_print == 'none' ) { } return( list( "analytic" = analytic_grad, "finite_difference" = finite_diff_grad, "relative_error" = relative_error, "flag_derivative_warning" = flag_derivative_warning ) ) } nloptr/R/cobyla.R0000644000176200001440000000372712367224754013412 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: cobyla.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using COBYLA, BOBYQA, and NEWUOA. cobyla <- function(x0, fn, lower = NULL, upper = NULL, hin = NULL, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LN_COBYLA" f1 <- match.fun(fn) fn <- function(x) f1(x, ...) if (!is.null(hin)) { f2 <- match.fun(hin) hin <- function(x) (-1)*f2(x, ...) # NLOPT expects hin <= 0 } S0 <- nloptr(x0, eval_f = fn, lb = lower, ub = upper, eval_g_ineq = hin, opts = opts) if (nl.info) print(S0) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } 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) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } newuoa <- function(x0, fn, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LN_NEWUOA" fun <- match.fun(fn) fn <- function(x) fun(x, ...) S0 <- nloptr(x0, fn, opts = opts) if (nl.info) print(S0) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } nloptr/R/tnewton.R0000644000176200001440000000261012367224754013625 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: tnewton.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Preconditioned Truncated Newton. 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) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } nloptr/R/varmetric.R0000644000176200001440000000216512367224754014130 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: varmetric.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Varmetric. varmetric <- function(x0, fn, gr = NULL, rank2 = TRUE, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) if (rank2) opts["algorithm"] <- "NLOPT_LD_VAR2" else opts["algorithm"] <- "NLOPT_LD_VAR1" fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (is.null(gr)) { gr <- function(x) nl.grad(x, fn) } else { .gr <- match.fun(gr) gr <- function(x) .gr(x, ...) } S0 <- nloptr(x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } nloptr/R/direct.R0000644000176200001440000000352212367224754013404 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: direct.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Direct. 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) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } directL <- function(fn, lower, upper, randomized = FALSE, original = FALSE, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) if (randomized) { opts["algorithm"] <- "NLOPT_GN_DIRECT_L_RAND" } else { opts["algorithm"] <- "NLOPT_GN_DIRECT_L" } if (original) opts["algorithm"] <- "NLOPT_GN_ORIG_DIRECT_L" fun <- match.fun(fn) fn <- function(x) fun(x, ...) x0 <- (lower + upper) / 2 S0 <- nloptr(x0, eval_f = fn, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } nloptr/R/mlsl.R0000644000176200001440000000304112367224754013075 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: mlsl.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Multi-Level Single-Linkage. # # CHANGELOG: # 05/05/2014: Replaced cat by warning. 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.") gr <- NULL } S0 <- nloptr(x0 = x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } nloptr/R/nloptr.R0000644000176200001440000003043612367224754013454 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # 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 Ipopt # ... : 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: # 13/01/2011: added print_level option # 24/07/2011: added finite difference gradient checker # 07/08/2011: moved addition of default options to separate function # show documentation of options if print_options_doc == TRUE # 05/05/2014: Replaced cat by message, so messages can now be suppressed by suppressMessages. 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(), ... ) { # internal function to check the arguments of the functions .checkfunargs = function( fun, arglist, funname ) { if( !is.function(fun) ) stop(paste(funname, " must be a function\n", sep = "")) flist = formals(fun) if ( length(flist) > 1 ) { fnms = names(flist)[2:length(flist)] # remove first argument, which is x rnms = names(arglist) m1 = match(fnms, rnms) if( any(is.na(m1)) ){ mx1 = which( is.na(m1) ) for( i in 1:length(mx1) ){ stop(paste(funname, " requires argument '", fnms[mx1[i]], "' but this has not been passed to the 'nloptr' function.\n", sep = "")) } } m2 = match(rnms, fnms) if( any(is.na(m2)) ){ mx2 = which( is.na(m2) ) for( i in 1:length(mx2) ){ stop(paste(rnms[mx2[i]], "' passed to (...) in 'nloptr' but this is not required in the ", funname, " function.\n", sep = "")) } } } return( 0 ) } # 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 ) { return( 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 ) { return( 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 ) { return( 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" ], ", " ) ) # run derivative checker if ( opts$check_derivatives ) { if ( opts$algorithm %in% list_algorithms[ grep( "NLOPT_[G,L]N", list_algorithms ) ] ) { warning( paste("Skipping derivative checker because algorithm '", opts$algorithm, "' does not use gradients.", sep='') ) } else { # check derivatives of objective function message( "Checking gradients of objective function." ) check.derivatives( .x = x0, func = function( x ) { eval_f_wrapper( x )$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$termination_conditions <- termination_conditions # check whether we have a correctly formed ipoptr object is.nloptr( ret ) # choose correct minimzation function based on wether constrained were supplied solution <- .Call( NLoptR_Optimize, ret ) # remove the environment from the return object ret$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='.' ) return( ret ) } nloptr/R/auglag.R0000644000176200001440000000576312367224754013403 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: auglag.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Augmented Lagrangian. auglag <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, heq = NULL, heqjac = NULL, localsolver = c("COBYLA"), localtol = 1e-6, ineq2local = FALSE, nl.info = FALSE, control = list(), ...) { if (ineq2local) { # gsolver <- "NLOPT_LN_AUGLAG_EQ" stop("Inequalities to local solver: feature not yet implemented.") } localsolver <- toupper(localsolver) if (localsolver %in% c("COBYLA")) { # derivative-free dfree <- TRUE gsolver <- "NLOPT_LN_AUGLAG" lsolver <- paste("NLOPT_LN_", localsolver, sep = "") } else if (localsolver %in% c("LBFGS", "MMA", "SLSQP")) { # with derivatives dfree <- FALSE gsolver <- "NLOPT_LD_AUGLAG" lsolver <- paste("NLOPT_LD_", localsolver, sep = "") } 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)) { .hin <- match.fun(hin) hin <- function(x) (-1) * .hin(x) # change hin >= 0 to hin <= 0 ! } if (!dfree) { if (is.null(hinjac)) { hinjac <- function(x) nl.jacobian(x, hin) } else { .hinjac <- match.fun(hinjac) hinjac <- function(x) (-1) * .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) S1 <- list( par = S0$solution, value = S0$objective, iter = S0$iterations, global_solver = gsolver, local_solver = lsolver, convergence = S0$status, message = S0$message) return(S1) } nloptr/R/nloptions.R0000644000176200001440000000272312367224754014161 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: nloptions.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Function to define nloptr options list. 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 list of named (character) objects.") namc <- match.arg(names(optlist), choices=names(opts), several.ok=TRUE) if (!all(names(optlist) %in% names(opts))) warning("Unknown names in control: ", names(optlist)[!(names(optlist) %in% names(opts))]) if (!is.null(namc)) opts[namc] <- optlist[namc] if ("algorithm" %in% namc) { warning("Option 'algorithm can not be set here; will be overwritten.") opts["algorithm"] <- NULL } return(opts) } nloptr/R/finite.diff.R0000644000176200001440000000267712367224754014331 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: finite.diff.R # Author: Jelmer Ypma # Date: 24 July 2011 # # 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 approcximation 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=1:length(.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, ... ) return( ( fx_prime - fx )/stepSizeVec[i] ) } grad_fx <- sapply (indices, approx.gradf.index, .x=.x, func=func, fx=fx, stepSizeVec=stepSizeVec, ... ) return( grad_fx ) } nloptr/R/nm.R0000644000176200001440000000245312367224754012546 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: nm.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Nelder-Mead and Subplex. 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) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } sbplx <- function(x0, fn, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ...) { opts <- nl.opts(control) opts["algorithm"] <- "NLOPT_LN_SBPLX" fun <- match.fun(fn) fn <- function(x) fun(x, ...) S0 <- nloptr(x0, fn, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } nloptr/R/lbfgs.R0000644000176200001440000000201612367224754013224 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: lbfgs.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using Low-storage BFGS. 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) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } nloptr/R/print.nloptr.R0000644000176200001440000000525612367224754014611 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: print.nloptr.R # Author: Jelmer Ypma # Date: 10 June 2010 # # This function prints some basic output of a nloptr # ojbect. The information is only available after it # has been solved. # # show.controls is TRUE, FALSE or a vector of indices. # Use this option to show none, or only a subset of # the controls. # # 13/01/2011: added show.controls option # 07/08/2011: show 'optimal value' instead of 'current value' if status == 1, 2, 3, or 4 print.nloptr <- function(x, show.controls=TRUE, ...) { cat( "\nCall:\n", deparse(x$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$message, ")\n" ),' ')), fill=TRUE ) cat( paste( "Number of Iterations....:", x$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$num_constraints_eq, "\n" ) ) # if show.controls is TRUE or FALSE, show all or none of the controls if ( is.logical( show.controls ) ) { # show all control variables if ( show.controls ) { controls.indices = 1:length(x$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/nloptr.get.default.options.R0000644000176200001440000002022612367224754017343 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # 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: # 12/07/2014: Changed from creating a data.frame to a function returning a data.frame. nloptr.get.default.options <- function() { dat.opts <- data.frame( rbind( c("algorithm", "character", "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_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_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", "none", FALSE, "This option is required. Check the NLopt website for a description of the algorithms."), c("stopval", "numeric", "-Inf <= stopval <= Inf", "-Inf", TRUE, "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, "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, "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, "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, "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, "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, "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, "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, "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 equality constraints are set to 1e-8."), c("print_level", "interger", "0, 1, 2, or 3", "0", FALSE, "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, "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, "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, "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, "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, "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("ranseed", "integer", "ranseed is a positive integer", "0", FALSE, "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" ) return( dat.opts ) }nloptr/R/gradients.R0000644000176200001440000000242712367224754014115 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: gradients.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Functions to calculate numerical Gradient and Jacobian. nl.grad <- function (x0, fn, heps = .Machine$double.eps^(1/3), ...) { if (!is.numeric(x0)) stop("Argument 'x0' must be a numeric value.") fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (length(fn(x0)) != 1) stop("Function 'f' must be a univariate function of 2 variables.") n <- length(x0) hh <- rep(0, n) gr <- numeric(n) for (i in 1:n) { hh[i] <- heps gr[i] <- (fn(x0 + hh) - fn(x0 - hh)) / (2*heps) hh[i] <- 0 } return(gr) } nl.jacobian <- function(x0, fn, heps = .Machine$double.eps^(1/3), ...) { if (!is.numeric(x0) || length(x0) == 0) stop("Argument 'x' must be a non-empty numeric vector.") fun <- match.fun(fn) fn <- function(x) fun(x, ...) n <- length(x0) m <- length(fn(x0)) jacob <- matrix(NA, m, n) hh <- numeric(n) for (i in 1:n) { hh[i] <- heps jacob[, i] <- (fn(x0 + hh) - fn(x0 - hh)) / (2*heps) hh[i] <- 0 } return(jacob) } nloptr/R/nloptr.add.default.options.R0000644000176200001440000000652212367224754017317 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: nloptr.print.options.R # Author: Jelmer Ypma # Date: 7 August 2011 # # 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. nloptr.add.default.options <- function( opts.user, x0=0, num_constraints_ineq=0, num_constraints_eq=0 ) { nloptr.default.options <- nloptr.get.default.options() # get names of options that define a termination condition termination.opts <- nloptr.default.options[ nloptr.default.options$is_termination_condition==TRUE, "name" ] if ( sum(termination.opts %in% names( opts.user )) == 0 ) { # get default xtol_rel xtol_rel_default <- as.numeric( nloptr.default.options[ nloptr.default.options$name=="xtol_rel", "default" ] ) warning( paste("No termination criterium specified, using default (relative x-tolerance = ", xtol_rel_default, ")", sep='') ) termination_conditions <- paste("relative x-tolerance = ", xtol_rel_default, " (DEFAULT)", sep='') } else { conv_options <- unlist(opts.user[names(opts.user) %in% termination.opts]) termination_conditions <- paste( paste( names(conv_options) ), ": ", paste( conv_options ), sep='', 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[ nloptr.default.options$type=="character", "name" ] opts.user <- sapply( 1:nrow(nloptr.default.options), function(i) { tmp.opts.name <- nloptr.default.options[i,"name"] # get user defined value it it's defined # otherwise use default value tmp.value <- ifelse( is.null(opts.user[[tmp.opts.name]]), nloptr.default.options[i,"default"], opts.user[[tmp.opts.name]] ) # paste options together in named list eval( parse( text=paste( "list('", tmp.opts.name, "'=", # add quotes around value if it's a character option ifelse( tmp.opts.name %in% nloptr.list.character.options, paste("'", tmp.value, "'", sep=''), tmp.value ), ")", sep="" ) ) ) } ) return( list( "opts.user" = opts.user, "termination_conditions" = termination_conditions ) ) } nloptr/R/nloptr.print.options.R0000644000176200001440000000363312367224754016300 0ustar liggesusers# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # File: nloptr.print.options.R # Author: Jelmer Ypma # Date: 8 August 2011 # # Print list of all options with description. # # Input: # opts.show: the description of the options in this list are shown (optional, default is to show all options) # opts.user: list with user defined options (optional) # Output: options, default values, user values if supplied) # and description printed to screen. No return value. # # 08/08/2011: Added opts.show argument to only show a subset of all options. nloptr.print.options <- function( opts.show=NULL, opts.user=NULL ) { # show all options if no list of options is supplied if ( is.null( opts.show ) ) { nloptr.show.options <- nloptr.get.default.options() } else { nloptr.show.options <- nloptr.get.default.options() nloptr.show.options <- nloptr.show.options[ nloptr.show.options$name %in% opts.show, ] } # loop over all options and print values for( row.cnt in 1: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/is.nloptr.R0000644000176200001440000002177312367224754014072 0ustar liggesusers# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved. # This code is published under the L-GPL. # # 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 # 16/06/2011: separated local optimzer check and equality constraints check # 05/05/2014: Replaced cat by warning. is.nloptr <- function( x ) { # Check whether the object exists and is a list if( is.null(x) ) { return( FALSE ) } if( !is.list(x) ) { return( FALSE ) } # 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) ) { if ( !is.function(x$eval_g_ineq) ) { stop('eval_g_ineq is not a function') } } if ( !is.null(x$eval_g_eq) ) { if ( !is.function(x$eval_g_eq) ) { stop('eval_g_eq is not a function') } } # Check whether bounds are defined for all controls if ( any( is.na( x$x0 ) ) ) { stop('x0 contains NA') } if ( length( x$x0 ) != length( x$lower_bounds ) ) { stop('length(lb) != length(x0)') } if ( length( x$x0 ) != length( x$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", "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_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" ) # check if an existing algorithm was supplied if ( !( x$options$algorithm %in% list_algorithms ) ) { stop( paste('Incorrect algorithm supplied. Use one of the following:\n', paste( list_algorithms, collapse='\n' ) ) ) } # determine subset of algorithms that need a derivative list_algorithmsD <- list_algorithms[ grep( "NLOPT_[G,L]D", list_algorithms ) ] list_algorithmsN <- 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$objective ) ) { stop('objective in x0 returns NA') } if ( any( is.na( f0$gradient ) ) ) { stop('gradient of objective in x0 returns NA') } if ( length( f0$gradient ) != length( x$x0 ) ) { stop('wrong number of elements in gradient of objective') } # check whether algorihtm needs a derivative if ( x$options$algorithm %in% list_algorithmsN ) { warning( 'a gradient was supplied for the objective function, but algorithm ', x$options$algorithm, ' does not use gradients.' ) } } else { if ( is.na( f0 ) ) { stop('objective in x0 returns NA') } # check whether algorihtm needs a derivative if ( x$options$algorithm %in% list_algorithmsD ) { stop( paste( '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$x0 ) if ( is.list( g0_ineq ) ) { if ( any( is.na( g0_ineq$constraints ) ) ) { stop('inequality constraints in x0 returns NA') } if ( any( is.na( g0_ineq$jacobian ) ) ) { stop('jacobian of inequality constraints in x0 returns NA') } if ( length( g0_ineq$jacobian ) != length( g0_ineq$constraints )*length( x$x0 ) ) { stop(paste('wrong number of elements in jacobian of inequality constraints (is ', length( g0_ineq$jacobian ), ', but should be ', length( g0_ineq$constraints ), ' x ', length( x$x0 ), ' = ', length( g0_ineq$constraints )*length( x$x0 ), ')', sep='')) } # check whether algorihtm needs a derivative if ( x$options$algorithm %in% list_algorithmsN ) { warning( 'a gradient was supplied for the inequality constraints, but algorithm ', x$options$algorithm, ' does not use gradients.' ) } } else { if ( any( is.na( g0_ineq ) ) ) { stop('inequality constraints in x0 returns NA') } # check whether algorihtm needs a derivative if ( x$options$algorithm %in% list_algorithmsD ) { stop( paste( 'A gradient for the inequality constraints is needed by algorithm', x$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 ( any( is.na( g0_eq$constraints ) ) ) { stop('equality constraints in x0 returns NA') } if ( any( is.na( g0_eq$jacobian ) ) ) { stop('jacobian of equality constraints in x0 returns NA') } if ( length( g0_eq$jacobian ) != length( g0_eq$constraints )*length( x$x0 ) ) { stop(paste('wrong number of elements in jacobian of equality constraints (is ', length( g0_eq$jacobian ), ', but should be ', length( g0_eq$constraints ), ' x ', length( x$x0 ), ' = ', length( g0_eq$constraints )*length( x$x0 ), ')', sep='')) } # check whether algorihtm needs a derivative if ( x$options$algorithm %in% list_algorithmsN ) { warning( 'a gradient was supplied for the equality constraints, but algorithm ', x$options$algorithm, ' does not use gradients.' ) } } else { if ( any( is.na( g0_eq ) ) ) { stop('equality constraints in x0 returns NA') } # check whether algorihtm needs a derivative if ( x$options$algorithm %in% list_algorithmsD ) { stop( paste( '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$num_constraints_eq > 0 ) { eq_algorithms <- c("NLOPT_LD_AUGLAG", "NLOPT_LN_AUGLAG", "NLOPT_LD_AUGLAG_EQ", "NLOPT_LN_AUGLAG_EQ", "NLOPT_GN_ISRES", "NLOPT_LD_SLSQP") if( !( x$options$algorithm %in% eq_algorithms ) ) { stop(paste('If you want to use equality constraints, then you should use one of these algorithms', paste(eq_algorithms, collapse=', '))) } } # check if a local optimizer was supplied, which is needed by some algorithms if ( x$options$algorithm %in% c("NLOPT_LD_AUGLAG", "NLOPT_LN_AUGLAG", "NLOPT_LD_AUGLAG_EQ", "NLOPT_LN_AUGLAG_EQ", "NLOPT_GN_MLSL", "NLOPT_GD_MLSL", "NLOPT_GN_MLSL_LDS", "NLOPT_GD_MLSL_LDS") ) { if ( is.null( x$local_options ) ) { stop(paste('The algorithm', x$options$algorithm, 'needs a local optimizer; specify an algorithm and termination condition in local_opts')) } } return( TRUE ) } nloptr/R/global.R0000644000176200001440000000643412367224754013377 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: global.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using StoGo. #-- Does not work: maybe C++ support missing? ---------------------- StoGo --- stogo <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, maxeval = 10000, xtol_rel = 1e-6, randomized = FALSE, nl.info = FALSE, ...) # control = list() { # opts <- nl.opts(control) 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) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } #-- Supports nonlinear constraints: quite inaccurate! -------------- ISRES --- isres <- function(x0, fn, lower, upper, hin = NULL, heq = NULL, maxeval = 10000, pop.size = 20*(length(x0)+1), xtol_rel = 1e-6, nl.info = FALSE, ...) { #opts <- nl.opts(control) opts <- list() opts$maxeval <- maxeval opts$xtol_rel <- xtol_rel opts$population <- pop.size opts$algorithm <- "NLOPT_GN_ISRES" fun <- match.fun(fn) fn <- function(x) fun(x, ...) if (!is.null(hin)) { .hin <- match(hin) hin <- function(x) (-1) * .hin(x) # change hin >= 0 to hin <= 0 ! } if (!is.null(heq)) { .heq <- match.fun(heq) heq <- function(x) .heq(x) } S0 <- nloptr(x0 = x0, eval_f = fn, lb = lower, ub = upper, eval_g_ineq = hin, eval_g_eq = heq, opts = opts) if (nl.info) print(S0) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } #-- ------------------------------------------------------------------ CRS --- crs2lm <- function(x0, fn, lower, upper, maxeval = 10000, pop.size = 10*(length(x0)+1), ranseed = NULL, xtol_rel = 1e-6, nl.info = FALSE, ...) { #opts <- nl.opts(control) opts <- list() opts$maxeval <- maxeval opts$xtol_rel <- xtol_rel opts$population <- pop.size if (!is.null(ranseed)) opts$ranseed <- as.integer(ranseed) opts$algorithm <- "NLOPT_GN_CRS2_LM" fun <- match.fun(fn) fn <- function(x) fun(x, ...) S0 <- nloptr(x0, eval_f = fn, lb = lower, ub = upper, opts = opts) if (nl.info) print(S0) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } nloptr/R/mma.R0000644000176200001440000000275212367224754012710 0ustar liggesusers# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved. # This code is published under the L-GPL. # # File: mma.R # Author: Hans W. Borchers # Date: 27 January 2014 # # Wrapper to solve optimization problem using MMA. mma <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, nl.info = FALSE, control = list(), ...) { 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)) { .hin <- match.fun(hin) hin <- function(x) (-1) * .hin(x) # change hin >= 0 to hin <= 0 ! if (is.null(hinjac)) { hinjac <- function(x) nl.jacobian(x, hin) } else { .hinjac <- match.fun(hinjac) hinjac <- function(x) (-1) * .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) S1 <- list(par = S0$solution, value = S0$objective, iter = S0$iterations, convergence = S0$status, message = S0$message) return(S1) } nloptr/vignettes/0000755000176200001440000000000012367224773013615 5ustar liggesusersnloptr/vignettes/reflist.bib0000644000176200001440000000367412367224755015755 0ustar liggesusers@MISC{NLopt:website, author = {Steven G. Johnson}, title = {The {N}{L}opt nonlinear-optimization package}, note = {\texttt{http://ab-initio.mit.edu/nlopt}} } @inproceedings{Leisch2002, author = {Friedrich Leisch}, title = {Sweave: Dynamic Generation of Statistical Reports Using Literate Data Analysis}, booktitle = {Compstat 2002 --- Proceedings in Computational Statistics}, pages = {575--580}, year = 2002, editor = {Wolfgang H{\"a}rdle and Bernd R{\"o}nz}, publisher = {Physica Verlag, Heidelberg}, note = {ISBN 3-7908-1517-9}, url = {http://www.stat.uni-muenchen.de/~leisch/Sweave} } @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} } nloptr/vignettes/nloptr.Rnw0000644000176200001440000003705612367224755015636 0ustar liggesusers\documentclass[a4paper]{article} \usepackage[round,authoryear,sort&compress]{natbib} \usepackage[english]{babel} \usepackage{graphicx} % \VignetteIndexEntry{Introduction to nloptr: an R interface to NLopt} % \VignetteKeyword{optimize} % \VignetteKeyword{interface} \SweaveOpts{keep.source=TRUE} \SweaveOpts{prefix.string = figs/plot, eps = FALSE, pdf = TRUE, tikz = FALSE} \title{Introduction to \texttt{nloptr}: an R interface to NLopt \thanks{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 \texttt{Sweave} (Leisch, 2002). 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.}} \author{Jelmer Ypma} \begin{document} \maketitle \nocite{Leisch2002} \DefineVerbatimEnvironment{Sinput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} <>= # 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)))) @ \begin{abstract} This document describes how to use \texttt{nloptr}, which is 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. \end{abstract} \nocite{NLopt:website} \section{Introduction} NLopt addresses general nonlinear optimization problems of the form: \begin{eqnarray*} &&\min_{x \in R^n} f(x) \\ &s.t.& g(x) \leq 0 \\ && h(x) = 0 \\ && x_L \leq x \leq x_U \end{eqnarray*} 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 can be specified in $g(\cdot)$, and equality constraints that can 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 avialable. Some of the information here has been taken from the NLopt website\footnote{\texttt{http://ab-initio.mit.edu/nlopt}}, where more details are available. All credit for implementing the C code for the different algorithms availalbe in NLopt should go to the respective authors. See the website\footnote{\texttt{http://ab-initio.mit.edu/wiki/index.php/Citing\_NLopt}} for information on how to cite NLopt and the algorithms you use. \section{Installation} This package is on CRAN and can be installed from within R using <>= install.packages("nloptr") @ You should now be able to load the R interface to NLopt and read the help. <>= library('nloptr') ?nloptr @ The most recent experimental version of \texttt{nloptr} can be installed from R-Forge using <>= install.packages("nloptr",repos="http://R-Forge.R-project.org") @ or from source using <>= install.packages("nloptr",type="source",repos="http://R-Forge.R-project.org") @ \section{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 \texttt{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) { return( 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2 ) } ## Gradient of Rosenbrock Banana function 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]) ) ) } @ We define initial values <>= # initial values x0 <- c( -1.2, 1 ) @ and then minimize the function using the \texttt{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 \citep{Nocedal:1980, LiuNocedal:1989}. The characters \texttt{LD} in the algorithm show that this algorithm looks for local minima (\texttt{L}) using a derivative-based (\texttt{D}) algorithm. Other algorithms look for global (\texttt{G}) minima, or they don't need derivatives (\texttt{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 ) @ 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] return( 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 ) @ This gives the same results as before. \section{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{eqnarray*} &&\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{eqnarray*} 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{eqnarray*} ( a_1 x_1 + b_1 )^3 - x_2 &\leq& 0 \\ ( a_2 x_1 + b_2 )^3 - x_2 &\leq& 0. \end{eqnarray*} First we define R functions to calculate the objective function and its gradient <>= # objective function eval_f0 <- function( x, a, b ){ return( sqrt(x[2]) ) } # gradient of objective function eval_grad_f0 <- function( x, a, b ){ return( c( 0, .5/sqrt(x[2]) ) ) } @ If needed, these can of course be calculated in the same function as before. Then we define the two constraints and the jacobian of the constraints <>= # constraint function eval_g0 <- function( x, a, b ) { return( (a*x[1] + b)^3 - 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 ) ) ) } @ Note that all of the functions above depend on additional parameters, \texttt{a} and \texttt{b}. We have to supply specific values for these when we invoke the optimization command. The constraint function \texttt{eval\_g0} returns a vector with in this case the same length as the vectors \texttt{a} and \texttt{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 ) print( res0 ) @ Here we supplied lower bounds for $x_2$ in \texttt{lb}. There are no upper bounds for both control variables, so we supply \texttt{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 \texttt{eval\_g\_ineq} and \texttt{eval\_jac\_g\_ineq}. Not all algorithms can handle inequality constraints, so we have to specifiy one that does, \texttt{NLOPT\_LD\_MMA} \citep{Svanberg:2002}. We also specify the option \texttt{print\_level} to obtain output during the optimization process. For the available \texttt{print\_level} values, see \texttt{?nloptr}. Setting the \texttt{check\_derivatives} option to \texttt{TRUE}, compares the gradients supplied by the user with a finite difference approximation in the initial point (\texttt{x0}). When this check is run, the option \texttt{check\_derivatives\_print} can be used to print all values of the derivative checker (\texttt{all} (default)), only those values that result in an error (\texttt{errors}) or no output (\texttt{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 \texttt{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, \texttt{a} and \texttt{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 \texttt{NLOPT\_LN\_COBYLA}, which is an algorithm that doesn't need gradient information \citep{Powell:1994, Powell: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 ) @ \section{Derivative checker} The derivative checker can be called when supplying a minimization problem to \texttt{nloptr}, using the options \texttt{check\_derivatives}, \texttt{check\_derivatives\_tol} and \texttt{check\_derivatives\_print}, but it can also be used separately. For example, define the function \texttt{g}, with vector outcome, and its gradient \texttt{g\_grad} <>= g <- function( x, a ) { return( 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 ) { return( 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 ) ) ) } @ \texttt{a} is some vector containing data. The gradient contains some errors in this case. By calling the function \texttt{check.derivatives} we can check the user-supplied analytic gradients with a finite difference approximation at a point \texttt{.x}. <>= res <- check.derivatives( .x=c(1,2), func=g, func_grad=g_grad, check_derivatives_print='all', a=c(.3, .8) ) @ The errors are shown on screen, where the option \texttt{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 @ Note that not all errors will be picked up by the derivative checker. For instance, if we run the check with \texttt{a = c(.5, .5)}, one of the errors is not flagged as an error. \section{Notes} The \texttt{.R} scripts in the \texttt{tests} directory contain more examples. For instance, \texttt{hs071.R} and \texttt{systemofeq.R} show how to solve problems with equality constraints. See also \texttt{http://ab-initio.mit.edu/wiki/index.php/NLopt\_Algorithms\#Augmented\_Lagrangian\_algorithm} for more details. Please let me know if you're missing any of the features that are implemented in NLopt. Sometimes the optimization procedure terminates with a message \texttt{maxtime was reached} without evaluating the objective function. Submitting the same problem again usually solves this problem. \bibliographystyle{plainnat} \bibliography{reflist} \appendix \section{Description of options} \label{sec:descoptions} <>= nloptr.print.options() @ \end{document} nloptr/README.md0000644000176200001440000001107012367224754013062 0ustar liggesusers# nloptr [![Build Status](https://travis-ci.org/jyypma/nloptr.svg?branch=master)](https://travis-ci.org/jyypma/nloptr) `nloptr` is an R interface to [NLopt](http://ab-initio.mit.edu/wiki/index.php/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. It can be used to solve general nonlinear programming problems with nonlinear constraints and lower and upper bounds for the controls, such as ``` min f(x) x in R^n s.t. g(x) <= 0 h(x) = 0 lb <= x <= ub ``` The NLopt library is available under the GNU Lesser General Public License (LGPL), and the copyrights are owned by a variety of authors. See the [website](http://ab-initio.mit.edu/wiki/index.php/Citing_NLopt) for information on how to cite NLopt and the algorithms you use. The R interface to NLopt, also under LGPL, can be downloaded from [CRAN](http://cran.r-project.org/web/packages/nloptr/index.html) or [GitHub](https://github.com/jyypma/nloptr) (development version). ## Installation For most versions of R `nloptr` can be installed from R with ``` install.packages('nloptr') ``` ### Development version The most recent (experimental) version can be installed from source from GitHub ``` library('devtools') install_github("jyypma/nloptr") ``` For this to work on Windows, you need to have Rtools and NLopt installed, and set an environment variable NLOPT_HOME with the location of the NLopt library. ## Disclaimer This package is distributed in the hope that it may be useful to some. The usual disclaimers apply (downloading and installing this software is at your own risk, and no support or guarantee is provided, I don't take liability and so on), but please let me know if you have any problems, suggestions, comments, etc. ## Files * [NLopt-2.4-win-build.zip](http://www.ucl.ac.uk/~uctpjyy/downloads/NLopt-2.4-win-build.zip) - static libraries of NLopt 2.4 compiled for Windows 32-bit and 64-bit. * [nloptr.pdf](http://cran.r-project.org/web/packages/nloptr/vignettes/nloptr.pdf) - an R vignette describing how to use the R interface to NLopt. * [INSTALL.windows](https://github.com/jyypma/nloptr/blob/master/INSTALL.windows) - description of how to install `nloptr` from source for Windows. ## Changelog A full version of the changelog can be found on [CRAN](http://cran.r-project.org/web/packages/nloptr/ChangeLog) | Date | Description | | :---------- | :----------- | | 27/01/2014 | Version 1.0.0 merged wrappers from the 'nloptwrap' package. | | 19/11/2013 | Version 0.9.6 Added a line in Makevars to replace some code in NLopt to fix compilation on Solaris as requested by Brian Ripley. | | 12/11/2013 | Version 0.9.5 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. | | 09/11/2013 | Version 0.9.4 updated NLopt to version 2.4. | | 31/07/2013 | Version 0.9.3 was a maintainance release. | | 11/07/2013 | Version 0.9.2 was a maintainance release. | | 31/04/2013 | Version 0.9.0 has a new `print_level = 3`, and is compiled with NLopt version 2.3 with `--with-cxx option`. This makes the StoGo algorithm available. | | 18/11/2011 | Version 0.8.9 removed some warnings from R CMD check and included some changes to the build process. | | 28/09/2011 | Version 0.8.8 updated to compile on Solaris. | | 03/09/2011 | Version 0.8.5 includes a working binary for MacOS. | | 12/08/2011 | Version 0.8.4 includes a new function `nloptr.print.options`, and has new options (`print_options_doc`, and `population` and `ranseed` for stochastic global solvers). | | 24/07/2011 | Version 0.8.3 has a finite difference derivative checker and includes checks to prevent adding constraints to a problem when the chosen algortihm does not allow for constraints. | | 09/07/2011 | Version 0.8.2 is on CRAN with an updated build process and a newer version of NLopt. | | 13/01/2011 | Version 0.8.1 contains an option print_level to control intermediate output. | ## Reference Steven G. 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Borchers and Dirk Eddelbuettel Maintainer: Jelmer Ypma Description: nloptr is 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 http://ab-initio.mit.edu/wiki/index.php/NLopt_Introduction for more information on the available algorithms. During installation on Unix the NLopt code is downloaded and compiled from the NLopt website. License: LGPL-3 Suggests: testthat (>= 0.8.1) LazyLoad: yes Packaged: 2014-08-02 18:12:19 UTC; Jelmer NeedsCompilation: yes Repository: CRAN Date/Publication: 2014-08-04 15:35:43 nloptr/configure0000755000176200001440000040305112367224754013516 0ustar liggesusers#! /bin/sh # Guess values for system-dependent variables and create Makefiles. # Generated by GNU Autoconf 2.69 for nloptr 1.0.1. # # # Copyright (C) 1992-1996, 1998-2012 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 -n "${ZSH_VERSION+set}" && (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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In this case, the evolution somewhat resembles a randomized Nelder-Mead algorithm. The published results for CRS seem to be largely empirical. } \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.} } \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). } \note{ The initial population size for CRS defaults to \code{10x(n+1)} in \code{n} dimensions, but this can be changed; the initial population must be at least \code{n+1}. } \examples{ ### Minimize the Hartmann6 function hartmann6 <- function(x) { n <- length(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 <- 0.0 for (i in 1:4) { fun <- fun - a[i] * exp(-sum(A[i,]*(x-B[i,])^2)) } return(fun) } 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)) ## Number of Iterations....: 4050 ## Termination conditions: maxeval: 10000 xtol_rel: 1e-06 ## Number of inequality constraints: 0 ## Number of equality constraints: 0 ## Optimal value of objective function: -3.32236801141328 ## Optimal value of controls: ## 0.2016893 0.1500105 0.4768738 0.2753326 0.3116516 0.6573004 } nloptr/man/varmetric.Rd0000644000176200001440000000441612367224754014647 0ustar liggesusers\name{varmetric} \alias{varmetric} \title{ Shifted Limited-memory Variable-metric } \description{ Shifted limited-memory variable-metric algorithm. } \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{\ldots}{further arguments to be passed to the function.} } \details{ Variable-metric methods are a variant of the quasi-Newton methods, especially adapted to large-scale unconstrained (or bound constrained) minimization. } \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.} } \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). } \note{ Based on L. Luksan's Fortran implementation of a shifted limited-memory variable-metric algorithm. } \seealso{ \code{\link{lbfgs}} } \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 } nloptr/man/check.derivatives.Rd0000644000176200001440000000466312367224754016260 0ustar liggesusers\name{check.derivatives} \alias{check.derivatives} \title{ Check analytic gradients of a function using finite difference approximations } \description{ This function compares the analytic gradients of a function with a finite difference approximation and prints the results of these checks. } \usage{ check.derivatives( .x, func, func_grad, check_derivatives_tol = 1e-04, check_derivatives_print = 'all', func_grad_name = 'grad_f', \ldots ) } \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. } \author{ Jelmer Ypma } \seealso{ \code{\link[nloptr:nloptr]{nloptr}} } \examples{ library('nloptr') # example with correct gradient f <- function( x, a ) { return( sum( ( x - a )^2 ) ) } f_grad <- function( x, a ) { return( 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 ) { return( 2*( x - a ) + c(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 ) { return( c( sum(x-a), sum( (x-a)^2 ) ) ) } g_grad <- function( x, a ) { return( rbind( rep(1,length(x)) + c(0,.01,rep(0,8)), 2*(x-a) + c(0,.1,rep(0,8)) ) ) } check.derivatives( .x=1:10, func=g, func_grad=g_grad, check_derivatives_print='all', a=runif(10) ) } \keyword{ optimize } \keyword{ interface } nloptr/man/cobyla.Rd0000644000176200001440000000566112367224754014127 0ustar liggesusers\name{cobyla} \alias{cobyla} \title{ Constrained Optimization by Linear Approximations } \description{ COBYLA is an algorithm for derivative-free optimization with nonlinear inequality and equality constraints (but see below). } \usage{ cobyla(x0, fn, lower = NULL, upper = NULL, hin = 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{hin}{function defining the inequality constraints, that is \code{hin>=0} for all components.} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{\ldots}{additional arguments passed to the function.} } \details{ It constructs successive linear approximations of the objective function and constraints via a simplex of n+1 points (in n dimensions), and optimizes these approximations in a trust region at each step. COBYLA supports equality constraints by transforming them into two inequality constraints. As this does not give full satisfaction with the implementation in NLOPT, it has not been made available here. } \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.} } \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. } \note{ The original code, written in Fortran by Powell, was converted in C for the Scipy project. } \seealso{ \code{\link{bobyqa}}, \code{\link{newuoa}} } \examples{ ### Solve Hock-Schittkowski no. 100 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) { h <- numeric(4) h[1] <- 127 - 2*x[1]^2 - 3*x[2]^4 - x[3] - 4*x[4]^2 - 5*x[5] h[2] <- 282 - 7*x[1] - 3*x[2] - 10*x[3]^2 - x[4] + x[5] h[3] <- 196 - 23*x[1] - x[2]^2 - 6*x[6]^2 + 8*x[7] h[4] <- -4*x[1]^2 - x[2]^2 + 3*x[1]*x[2] -2*x[3]^2 - 5*x[6] +11*x[7] return(h) } S <- cobyla(x0.hs100, fn.hs100, hin = hin.hs100, nl.info = TRUE, control = list(xtol_rel = 1e-8, maxeval = 2000)) ## Optimal value of objective function: 680.630057374431 } nloptr/man/sbplx.Rd0000644000176200001440000000434012367224754013777 0ustar liggesusers\name{sbplx} \alias{sbplx} \title{ Subplex Algorithm } \description{ Subplex is a variant of Nelder-Mead that uses Nelder-Mead on a sequence of subspaces. } \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{\ldots}{additional arguments passed to the function.} } \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). } \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.} } \references{ T. Rowan, ``Functional Stability Analysis of Numerical Algorithms'', Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin, 1990. } \note{ It is the request of Tom Rowan that reimplementations of his algorithm shall not use the name `subplex'. } \seealso{ \code{subplex::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 (?) } nloptr/man/nloptr.print.options.Rd0000644000176200001440000000225412367224754017014 0ustar liggesusers\name{nloptr.print.options} \alias{nloptr.print.options} \title{ Print description of nloptr options } \description{ This function prints a list of all the options that can be set when solving a minimization problem using \code{nloptr}. } \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}. } } \author{ Jelmer Ypma } \seealso{ \code{\link[nloptr:nloptr]{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 ) } \keyword{ optimize } \keyword{ interface } nloptr/man/isres.Rd0000644000176200001440000000550012367224754013773 0ustar liggesusers\name{isres} \alias{isres} \title{ Improved Stochastic Ranking Evolution Strategy } \description{ The Improved Stochastic Ranking Evolution Strategy (ISRES) algorithm for nonlinearly constrained global optimization (or at least semi-global: although it has heuristics to escape local optima. } \usage{ isres(x0, fn, lower, upper, hin = NULL, heq = NULL, maxeval = 10000, pop.size = 20*(length(x0)+1), xtol_rel = 1e-6, 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{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 NLopt info been shown.} \item{\ldots}{additional arguments passed to the function.} } \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 bound constraints. } \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.} } \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). } \note{ The initial population size for CRS defaults to \code{20x(n+1)} in \code{n} dimensions, but this can be changed; the initial population must be at least \code{n+1}. } \examples{ ### Rosenbrock Banana objective function fn <- function(x) return( 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2 ) x0 <- c( -1.2, 1 ) lb <- c( -3, -3 ) ub <- c( 3, 3 ) isres(x0 = x0, fn = fn, lower = lb, upper = ub) } nloptr/man/auglag.Rd0000644000176200001440000001266312367224754014116 0ustar liggesusers\name{auglag} \alias{auglag} \title{ Augmented Lagrangian Algorithm } \description{ The Augmented Lagrangian method adds additional terms to the unconstrained objective function, designed to emulate a Lagrangian multiplier. } \usage{ auglag(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, heq = NULL, heqjac = NULL, localsolver = c("COBYLA"), localtol = 1e-6, ineq2local = FALSE, 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 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 inequalty 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{\ldots}{additional arguments passed to the function.} } \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 ``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.) } \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.} } \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). } \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} } \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) auglag(x0, fn, gr = NULL, hin = hin, heq = heq) # with COBYLA # $par: 0.8228761 0.9114382 # $value: 1.393464 # $iter: 1001 auglag(x0, fn, gr = NULL, hin = hin, heq = heq, localsolver = "SLSQP") # $par: 0.8228757 0.9114378 # $value: 1.393465 # $iter 173 ## Example from the alabama::auglag help page 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 <- function(x) c(6*x[2] + 4*x[3] - x[1]^3 - 3, x[1], x[2], x[3]) auglag(runif(3), fn, hin = hin, heq = heq, localsolver="lbfgs") # $par: 2.380000e-09 1.086082e-14 1.000000e+00 # $value: 1 # $iter: 289 ## Powell problem from the Rsolnp::solnp help page 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]) auglag(x0, fn1, heq = eqn1, localsolver = "mma") # $par: -3.988458e-10 -1.654201e-08 -3.752028e-10 8.904445e-10 8.926336e-10 # $value: 1 # $iter: 1001 } nloptr/man/nloptr.get.default.options.Rd0000644000176200001440000000235112367224754020060 0ustar liggesusers\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. } \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}}. } \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).} } \author{ Jelmer Ypma } \seealso{ \code{\link[nloptr:nloptr]{nloptr}} \code{\link[nloptr:nloptr.print.options]{nloptr.print.options}} } \keyword{ optimize } \keyword{ interface } nloptr/man/bobyqa.Rd0000644000176200001440000000375112367224754014131 0ustar liggesusers\name{bobyqa} \alias{bobyqa} \title{ Bound Optimization by Quadratic Approximation } \description{ BOBYQA performs derivative-free bound-constrained optimization using an iteratively constructed quadratic approximation for the objective function. } \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 NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{\ldots}{additional arguments passed to the function.} } \details{ This is an algorithm derived from the BOBYQA Fortran subroutine of Powell, converted to C and modified for the NLOPT stopping criteria. } \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.} } \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). } \note{ Because 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}} } \examples{ fr <- function(x) { ## Rosenbrock Banana function 100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2 } (S <- bobyqa(c(0, 0, 0), fr, lower = c(0, 0, 0), upper = c(0.5, 0.5, 0.5))) } nloptr/man/newuoa.Rd0000644000176200001440000000353212367224754014147 0ustar liggesusers\name{newuoa} \alias{newuoa} \title{ New Unconstrained Optimization with quadratic Approximation } \description{ NEWUOA solves quadratic subproblems in a spherical trust regionvia a truncated conjugate-gradient algorithm. For bound-constrained problems, BOBYQA shold be used instead, as Powell developed it as an enhancement thereof for bound constraints. } \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 NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{\ldots}{additional arguments passed to the function.} } \details{ This is an algorithm derived from the NEWUOA Fortran subroutine of Powell, converted to C and modified for the NLOPT stopping criteria. } \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.} } \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). } \note{ NEWUOA may be largely superseded by BOBYQA. } \seealso{ \code{\link{bobyqa}}, \code{\link{cobyla}} } \examples{ fr <- function(x) { ## Rosenbrock Banana function 100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2 } (S <- newuoa(c(1, 2), fr)) } nloptr/man/mlsl.Rd0000644000176200001440000001023012367224754013611 0ustar liggesusers\name{mlsl} \alias{mlsl} \title{ Multi-level Single-linkage } \description{ The ``Multi-Level Single-Linkage'' (MLSL) algorithm for global optimization searches by a sequence of local optimizations from random starting points. A modification of MLSL is included using a low-discrepancy sequence (LDS) instead of pseudorandom numbers. } \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 NLopt info been shown.} \item{control}{list of options, see \code{nl.opts} for help.} \item{\ldots}{additional arguments passed to the function.} } \details{ MLSL is a `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 has some theoretical guarantees of finding all local optima in a finite number of local minimizations. The local-search portion of MLSL can use any of the other algorithms in NLopt, and in particular can use either gradient-based or derivative-free algorithms. For this wrapper only gradient-based \code{L-BFGS} is available as local method. } \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.} } \references{ A. H. G. Rinnooy Kan and G. T. Timmer, ``Stochastic global optimization methods'' Mathematical Programming, vol. 39, p. 27-78 (1987). Sergei Kucherenko and Yury Sytsko, ``Application of deterministic low-discrepancy sequences in global optimization,'' Computational Optimization and Applications, vol. 30, p. 297-318 (2005). } \note{ If you don't set a stopping tolerance for your local-optimization algorithm, MLSL defaults to \code{ftol_rel=1e-15} and \code{xtol_rel=1e-7} for the local searches. } \seealso{ \code{\link{direct}} } \examples{ ### Minimize the Hartmann6 function hartmann6 <- function(x) { n <- length(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 <- 0.0 for (i in 1:4) { fun <- fun - a[i] * exp(-sum(A[i,]*(x-B[i,])^2)) } return(fun) } 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)) ## 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: -3.32236801141552 ## Current value of controls: ## 0.2016895 0.1500107 0.476874 0.2753324 0.3116516 0.6573005 } nloptr/man/nloptions.Rd0000644000176200001440000000205012367224754014670 0ustar liggesusers\name{NLopt options} \alias{nl.opts} \title{ Setting NL Options } \description{ Sets and changes the NLOPT options. } \usage{ nl.opts(optlist = NULL) } \arguments{ \item{optlist}{list of options, see below.} } \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} } \value{ returns a list with default and changed options. } \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)) } nloptr/man/nloptr-package.Rd0000644000176200001440000001143512367224754015561 0ustar liggesusers\name{nloptr-package} \alias{nloptr-package} \docType{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{http://ab-initio.mit.edu/nlopt}{the NLopt website}, where more details are available. NLopt addresses general nonlinear optimization problems of the form: min f(x) x in R^n s.t. g(x) <= 0 h(x) = 0 lb <= x <= ub where f is the objective function to be minimized and x represents the n optimization parameters. This problem may optionally be subject to the bound constraints (also called box constraints), lb and ub. For partially or totally unconstrained problems the bounds can take -Inf or Inf. One may also optionally have m nonlinear inequality constraints (sometimes called a nonlinear programming problem), which can be specified in g(x), and equality constraints that can be specified in h(x). Note that not all of the algorithms in NLopt can handle constraints. An optimization problem can be solved with the general nloptr interface, or using one of the wrapper functions for the separate algorithms; auglag, bobyqa, cobyla, crs2lm, direct, lbfgs, mlsl, mma, neldermead, newuoa, sbplx, slsqp, stogo, tnewton, varmetric. } \details{ \tabular{ll}{ Package: \tab nloptr\cr Type: \tab Package\cr Version: \tab 0.9.9\cr Date: \tab 2013-11-22\cr License: \tab L-GPL\cr LazyLoad: \tab yes\cr } } \author{ Steven G. Johnson and others (C code) \cr Jelmer Ypma (R interface) \cr Hans W. Borchers (wrappers) } \references{ Steven G. Johnson, The NLopt nonlinear-optimization package, \url{http://ab-initio.mit.edu/nlopt} } \keyword{ optimize } \keyword{ interface } \seealso{ \code{\link{optim}} \code{\link{nlm}} \code{\link{nlminb}} \code{\link[Rsolnp:Rsolnp-package]{Rsolnp}} \code{\link[Rsolnp:solnp]{ssolnp}} \code{\link{nloptr}} \code{\link{auglag}} \code{\link{bobyqa}} \code{\link{cobyla}} \code{\link{crs2lm}} \code{\link{direct}} \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}} } \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 = (1.00000000, 4.74299963, 3.82114998, 1.37940829) library('nloptr') # # f(x) = x1*x4*(x1 + x2 + x3) + x3 # eval_f <- function( x ) { return( 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] ) return( 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] ) return( 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 ) } nloptr/man/tnewton.Rd0000644000176200001440000000456412367224754014355 0ustar liggesusers\name{tnewton} \alias{tnewton} \title{ Preconditioned Truncated Newton } \description{ Truncated Newton methods, also calledNewton-iterative methods, solve an approximating Newton system using a conjugate-gradient approach and are related to limited-memory BFGS. } \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{\ldots}{additional arguments passed to the function.} } \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. } \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.} } \references{ R. S. Dembo and T. Steihaug, ``Truncated Newton algorithms for large-scale optimization,'' Math. Programming 26, p. 190-212 (1982). } \note{ Less reliable than Newton's method, but can handle very large problems. } \seealso{ \code{\link{lbfgs}} } \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, 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 } nloptr/man/neldermead.Rd0000644000176200001440000000470612367224754014755 0ustar liggesusers\name{neldermead} \alias{neldermead} \title{ Nelder-Mead Simplex } \description{ An implementation of almost the original Nelder-Mead simplex algorithm. } \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{\ldots}{additional arguments passed to the function.} } \details{ Provides xplicit 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. } \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.} } \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). } \note{ The author of NLopt would tend to recommend the Subplex method instead. } \seealso{ \code{dfoptim::nmk} } \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 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} } nloptr/man/stogo.Rd0000644000176200001440000000434212367224754014004 0ustar liggesusers\name{stogo} \alias{stogo} \title{ Stochastic Global Optimization } \description{ StoGO is a global optimization algorithm that works by systematically dividing the search space into smaller hyper-rectangles. } \usage{ stogo(x0, fn, gr = NULL, lower = NULL, upper = NULL, maxeval = 10000, xtol_rel = 1e-6, randomized = FALSE, nl.info = FALSE, ...) } \arguments{ \item{x0}{initial point for searching the optimum.} \item{fn}{objective function that is to be minimized.} \item{gr}{optional gradient of the objective function.} \item{lower, upper}{lower and upper bound constraints.} \item{maxeval}{maximum number of function evaluations.} \item{xtol_rel}{stopping criterion for relative change reached.} \item{randomized}{logical; shall a randomizing variant be used?} \item{nl.info}{logical; shall the original NLopt info been shown.} \item{\ldots}{additional arguments passed to the function.} } \details{ 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 by a gradient-based local-search algorithm (a BFGS variant), optionally including some randomness. } \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.} } \references{ S. Zertchaninov and K. Madsen, ``A C++ Programme for Global Optimization,'' IMM-REP-1998-04, Department of Mathematical Modelling, Technical University of Denmark. } \note{ Only bound-constrained problems are supported by this algorithm. } \examples{ ### Rosenbrock Banana objective function fn <- function(x) return( 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2 ) x0 <- c( -1.2, 1 ) lb <- c( -3, -3 ) ub <- c( 3, 3 ) stogo(x0 = x0, fn = fn, lower = lb, upper = ub) } nloptr/man/is.nloptr.Rd0000644000176200001440000000123412367224754014576 0ustar liggesusers\name{is.nloptr} \alias{is.nloptr} \title{ R interface to NLopt } \description{ is.nloptr preforms checks to see if a fully specified problem is supplied to nloptr. Mostly for internal use. } \usage{ is.nloptr( x ) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{x}{ object to be tested. } } \value{ Logical. Return TRUE if all tests were passed, otherwise return FALSE or exit with Error. } \author{ Jelmer Ypma } \seealso{ \code{\link[nloptr:nloptr]{nloptr}} } % Add one or more standard keywords, see file 'KEYWORDS' in the % R documentation directory. \keyword{ optimize } \keyword{ interface } nloptr/man/print.nloptr.Rd0000644000176200001440000000166612367224754015330 0ustar liggesusers\name{print.nloptr} \alias{print.nloptr} \title{ Print results after running nloptr } \description{ This function prints the nloptr object that holds the results from a minimization using \code{nloptr}. } \usage{ \method{print}{nloptr}( x, show.controls=TRUE, \dots ) } \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. } } \author{ Jelmer Ypma } \seealso{ \code{\link[nloptr:nloptr]{nloptr}} } \keyword{ optimize } \keyword{ interface } nloptr/man/slsqp.Rd0000644000176200001440000000721312367224754014013 0ustar liggesusers\name{slsqp} \alias{slsqp} \title{ Sequential Quadratic Programming (SQP) } \description{ Sequential (least-squares) quadratic programming (SQP) algorithm for nonlinearly constrained, gradient-based optimization, supporting both equality and inequality constraints. } \usage{ slsqp(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = NULL, heq = NULL, heqjac = 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{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{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{\ldots}{additional arguments passed to the function.} } \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. } \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.} } \references{ Dieter Kraft, ``A software package for sequential quadratic programming'', Technical Report DFVLR-FB 88-28, Institut fuer Dynamik der Flugsysteme, Oberpfaffenhofen, July 1988. } \note{ See more infos at \url{http://ab-initio.mit.edu/wiki/index.php/NLopt_Algorithms}. } \seealso{ \code{alabama::auglag}, \code{Rsolnp::solnp}, \code{Rdonlp2::donlp2} } \examples{ ## Solve the Hock-Schittkowski problem no. 100 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) { h <- numeric(4) h[1] <- 127 - 2*x[1]^2 - 3*x[2]^4 - x[3] - 4*x[4]^2 - 5*x[5] h[2] <- 282 - 7*x[1] - 3*x[2] - 10*x[3]^2 - x[4] + x[5] h[3] <- 196 - 23*x[1] - x[2]^2 - 6*x[6]^2 + 8*x[7] h[4] <- -4*x[1]^2 - x[2]^2 + 3*x[1]*x[2] -2*x[3]^2 - 5*x[6] +11*x[7] return(h) } S <- slsqp(x0.hs100, fn = fn.hs100, # no gradients and jacobians provided hin = hin.hs100, control = list(xtol_rel = 1e-8, check_derivatives = TRUE)) S ## Optimal value of objective function: 690.622270249131 *** WRONG *** # Even the numerical derivatives seem to be too tight. # Let's try with a less accurate jacobian. hinjac.hs100 <- function(x) nl.jacobian(x, hin.hs100, heps = 1e-2) S <- slsqp(x0.hs100, fn = fn.hs100, hin = hin.hs100, hinjac = hinjac.hs100, control = list(xtol_rel = 1e-8)) S ## Optimal value of objective function: 680.630057392593 *** CORRECT *** } nloptr/man/gradients.Rd0000644000176200001440000000222312367224754014625 0ustar liggesusers\name{grad, jacobian} \alias{nl.grad} \alias{nl.jacobian} \title{ Numerical Gradients and Jacobians } \description{ Provides numerical gradients and jacobians. } \usage{ nl.grad(x0, fn, heps = .Machine$double.eps^(1/3), ...) nl.jacobian(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.} } \details{ Both functions apply the ``central difference formula'' with step size as recommended in the literature. } \value{ \code{grad} returns the gradient as a vector; \code{jacobian} returns the Jacobian as a matrix of usual dimensions. } \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 } nloptr/man/direct.Rd0000644000176200001440000001042312367224754014120 0ustar liggesusers\name{DIRECT} \alias{direct} \alias{directL} \title{ DIviding RECTangles Algorithm for Global Optimization } \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). } \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{randomized}{logical; shall some randomization be used to decide which dimension to halve next in the case of near-ties.} \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{\ldots}{additional arguments passed to the function.} } \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. } \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.} } \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). } \note{ The DIRECT_L algorithm should be tried first. } \seealso{ The \code{dfoptim} package will provide a pure R version of this algorithm. } \examples{ ### Minimize the Hartmann6 function hartmann6 <- function(x) { n <- length(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 <- 0.0 for (i in 1:4) { fun <- fun - a[i] * exp(-sum(A[i,]*(x-B[i,])^2)) } return(fun) } S <- directL(hartmann6, rep(0,6), rep(1,6), nl.info = TRUE, control=list(xtol_rel=1e-8, maxeval=1000)) ## Number of Iterations....: 500 ## Termination conditions: stopval: -Inf ## xtol_rel: 1e-08, maxeval: 500, 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 } nloptr/man/lbfgs.Rd0000644000176200001440000000501212367224754013741 0ustar liggesusers\name{lbfgs} \alias{lbfgs} \title{ Low-storage BFGS } \description{ Low-storage version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. } \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{\ldots}{further arguments to be passed to the function.} } \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}. } \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.} } \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). } \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}} } \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 } nloptr/man/mma.Rd0000644000176200001440000000717112367224754013426 0ustar liggesusers\name{mma} \alias{mma} \title{ Method of Moving Asymptotes } \description{ Globally-convergent method-of-moving-asymptotes (MMA) algorithm for gradient-based local optimization, including nonlinear inequality constraints (but not equality constraints). } \usage{ mma(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL, hinjac = 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{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{\ldots}{additional arguments passed to the function.} } \details{ This is an improved CCSA ("conservative convex separable approximation") variant of the original MMA algorithm published by Svanberg in 1987, which has become popular for topology optimization. Note: } \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.} } \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). } \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{slsqp}} } \examples{ ## Solve the Hock-Schittkowski problem no. 100 with analytic gradients 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) { h <- numeric(4) h[1] <- 127 - 2*x[1]^2 - 3*x[2]^4 - x[3] - 4*x[4]^2 - 5*x[5] h[2] <- 282 - 7*x[1] - 3*x[2] - 10*x[3]^2 - x[4] + x[5] h[3] <- 196 - 23*x[1] - x[2]^2 - 6*x[6]^2 + 8*x[7] h[4] <- -4*x[1]^2 - x[2]^2 + 3*x[1]*x[2] -2*x[3]^2 - 5*x[6] +11*x[7] return(h) } 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), 4, 7, byrow=TRUE) } # incorrect result with exact 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)) # correct result with inexact jacobian S <- mma(x0.hs100, fn.hs100, hin = hin.hs100, nl.info = TRUE, control = list(xtol_rel = 1e-8)) } nloptr/man/nloptr.Rd0000644000176200001440000002434312367224754014172 0ustar liggesusers\name{nloptr} \alias{nloptr} \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{http://ab-initio.mit.edu/nlopt}{the NLopt website}, where more details are available. NLopt addresses general nonlinear optimization problems of the form: min f(x) x in R^n s.t. g(x) <= 0 h(x) = 0 lb <= x <= ub where f is the objective function to be minimized and x represents the n optimization parameters. This problem may optionally be subject to the bound constraints (also called box constraints), lb and ub. For partially or totally unconstrained problems the bounds can take -Inf or Inf. One may also optionally have m nonlinear inequality constraints (sometimes called a nonlinear programming problem), which can be specified in g(x), and equality constraints that can be specified in h(x). Note that not all of the algorithms in NLopt can handle constraints. } \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(), ... ) } %- maybe also 'usage' for other objects documented here. \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 -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 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 "objective" 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 "objective" 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 "algorithm" is required. Check the \href{http://ab-initio.mit.edu/wiki/index.php/NLopt_Algorithms}{NLopt website} for a full list of available algorithms. Other options control the termination conditions (minf_max, ftol_rel, ftol_abs, xtol_rel, xtol_abs, maxeval, maxtime). Default is xtol_rel = 1e-4. More information \href{http://ab-initio.mit.edu/wiki/index.php/NLopt_Introduction\#Termination_conditions}{here}. A full description of all options is shown by the function \code{nloptr.print.options()}. Some algorithms with equality constraints require the option local_opts, which contains a list with an algorithm and a termination condition for the local algorithm. See ?`nloptr-package` for an example. The option 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 check_derivatives (default = FALSE) can be used to run to compare the analytic gradients with finite difference approximations. The option check_derivatives_print ('all' (default), 'errors', '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 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 op NLopt that was used} } \references{ Steven G. Johnson, The NLopt nonlinear-optimization package, \url{http://ab-initio.mit.edu/nlopt} } \author{ Steven G. Johnson and others (C code) \cr Jelmer Ypma (R interface) } \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{\link[Rsolnp:Rsolnp-package]{Rsolnp}} \code{\link[Rsolnp:solnp]{ssolnp}} } \note{See ?`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 ) } % Add one or more standard keywords, see file 'KEYWORDS' in the % R documentation directory. \keyword{ optimize } \keyword{ interface } nloptr/INSTALL.windows0000644000176200001440000000676012367224754014337 0ustar liggesusersThis file describes how to install nloptr from source for Windows. Compiling nloptr for Windows consists of two steps: 1. configure and compile NLopt from source or download and unpack a pre-compiled binary (NLopt-2.4-win-build.zip from http://www.ucl.ac.uk/~uctpjyy/nloptr.html) 2. compile the R interface *** To install NLopt from source (optional) Requirements: Cygwin or MSYS 1. Download the latest source of NLopt from http://ab-initio.mit.edu/wiki/index.php/NLopt#Download_and_installation, e.g. nlopt-2.4.tar.gz and unpack this archive somewhere (e.g. c:/tmp/nlopt-2.4). 2. Create a bash script somewhere, e.g. c:/tmp/NLoptInstall.sh with the following contents #!/bin/bash R_HOME="C:/tools/R/R-3.0.2" R_ARCH="i386" NLOPT_SRC_DIR="C:/tmp/nlopt-2.4" NLOPT_LIB_DIR="C:/tmp/nlopt" # Create directory for output mkdir ${NLOPT_LIB_DIR} mkdir ${NLOPT_LIB_DIR}/${R_ARCH} # Start in source directory cd ${NLOPT_SRC_DIR} # Get R compilers and flags CC=`"${R_HOME}/bin/${R_ARCH}/R.exe" CMD config CC` CFLAGS=`"${R_HOME}/bin/${R_ARCH}/R.exe" CMD config CFLAGS` CPP=`"${R_HOME}/bin/${R_ARCH}/R.exe" CMD config CPP` CPPFLAGS=`"${R_HOME}/bin/${R_ARCH}/R.exe" CMD config CPPFLAGS` CXX=`"${R_HOME}/bin/${R_ARCH}/R.exe" CMD config CXX` CXXFLAGS=`"${R_HOME}/bin/${R_ARCH}/R.exe" CMD config CXXFLAGS` CXXCPP=`"${R_HOME}/bin/${R_ARCH}/R.exe" CMD config CXXCPP` F77=`"${R_HOME}/bin/${R_ARCH}/R.exe" CMD config F77` FFLAGS=`"${R_HOME}/bin/${R_ARCH}/R.exe" CMD config FFLAGS` echo "./configure --prefix=\"${NLOPT_LIB_DIR}/${R_ARCH}\" --disable-shared --enable-static --without-octave --without-matlab --without-guile --without-python --with-cxx CC=\"${CC}\" ADD_CFLAGS=\"${CFLAGS}\" CPP=\"${CPP}\" ADD_CPPFLAGS=\"${CPPFLAGS}\" CXX=\"${CXX}\" ADD_CXXFLAGS=\"${CXXFLAGS}\" CXXCPP=\"${CXXCPP}\" F77=\"${F77}\" ADD_FFLAGS=\"${FFLAGS}\"" # Configure ./configure --prefix="${NLOPT_LIB_DIR}/${R_ARCH}" --disable-shared --enable-static --without-octave --without-matlab --without-guile --without-python --with-cxx CC="${CC}" ADD_CFLAGS="${CFLAGS}" CPP="${CPP}" ADD_CPPFLAGS="${CPPFLAGS}" CXX="${CXX}" ADD_CXXFLAGS="${CXXFLAGS}" CXXCPP="${CXXCPP}" F77="${F77}" ADD_FFLAGS="${FFLAGS}" # Compile make make install 3. In c:/tmp/NLoptInstall.sh adjust the values of the following macros R_HOME (The directory where R is located) NLOPT_SRC_DIR (The directory where the NLopt source is located, i.e. the directory created in 1.) NLOPT_LIB_DIR (The directory where the NLopt binary will be after compilation. This directory is created by the script NLoptInstall.sh) 4. Start MSYS, go to the directory where the script is located and execute the bash script > cd c:/tmp > ./NLoptInstall.sh The bash script sets macros for the correct compilers, as used by R, and configures and compiles the NLopt code. You do not need to use the script to compile NLopt, but it simplifies the process. 5. Optionally compile NLopt for 64-bit. Change the line R_ARCH="i386" to R_ARCH="x64" in c:/tmp/NLoptInstall.sh and execture the script again from MSYS. *** To install nloptr Requirements: Rtools 1. Download the source of nloptr (from R-forge https://r-forge.r-project.org/R/?group_id=933 or CRAN http://cran.r-project.org/web/packages/nloptr/index.html) and unpack this somewhere. 2. Before building from the MS-DOS prompt, define an enviroment variable with the location of the NLopt library, e.g. set NLOPT_HOME=c:/tmp/nlopt 3. Compile the R interface R CMD build nloptr/pkg nloptr/cleanup0000755000176200001440000000022612367224754013161 0ustar liggesusers#!/bin/sh rm -rf autom4te.cache/ config.log config.status \ src/Makevars src/*.o src/*.so src/*.dylib \ *~ \ nlopt-?.?.?/

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