R/mma.R

In jyypma/nloptr: R Interface to NLopt

# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved.
# SPDX-License-Identifier: LGPL-3.0-or-later
#
# File:   mma.R
# Author: Hans W. Borchers
# Date:   27 January 2014
#
# Wrapper to solve optimization problem using MMA.
# CHANGELOG
#
# 2023-02-09: Cleanup and tweaks for safety and efficiency (Avraham Adler)
#


#' Method of Moving Asymptotes
#'
#' Globally-convergent method-of-moving-asymptotes (MMA) algorithm for
#' gradient-based local optimization, including nonlinear inequality
#' constraints (but not equality constraints).
#'
#' 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:
#'
#' @param x0 starting point for searching the optimum.
#' @param fn objective function that is to be minimized.
#' @param gr gradient of function \code{fn}; will be calculated numerically if
#' not specified.
#' @param lower,upper lower and upper bound constraints.
#' @param hin function defining the inequality constraints, that is
#' \code{hin>=0} for all components.
#' @param hinjac Jacobian of function \code{hin}; will be calculated
#' numerically if not specified.
#' @param nl.info logical; shall the original NLopt info been shown.
#' @param control list of options, see \code{nl.opts} for help.
#' @param ... additional arguments passed to the function.
#'
#' @return List with components:
#'   \item{par}{the optimal solution found so far.}
#'   \item{value}{the function value corresponding to \code{par}.}
#'   \item{iter}{number of (outer) iterations, see \code{maxeval}.}
#'   \item{convergence}{integer code indicating successful completion (> 1)
#'   or a possible error number (< 0).}
#'   \item{message}{character string produced by NLopt and giving additional
#'   information.}
#'
#' @export mma
#'
#' @author Hans W. Borchers
#'
#' @note ``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}}
#'
#' @references Krister Svanberg, ``A class of globally convergent optimization
#' methods based on conservative convex separable approximations,'' SIAM J.
#' Optim. 12 (2), p. 555-573 (2002).
#'
#' @examples
#'
#' ##  Solve the Hock-Schittkowski problem no. 100 with analytic gradients
#' 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))
#'
#' \donttest{
#' # This example is put in donttest because it runs for more than
#' # 40 seconds under 32-bit Windows. The difference in time needed
#' # to execute the code between 32-bit Windows and 64-bit Windows
#' # can probably be explained by differences in rounding/truncation
#' # on the different systems. On Windows 32-bit more iterations
#' # are needed resulting in a longer runtime.
#' # correct result with inexact jacobian
#' S <- mma(x0.hs100, fn.hs100, hin = hin.hs100,
#'       nl.info = TRUE, control = list(xtol_rel = 1e-8))
#' }
#'
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)) {
    if (getOption("nloptr.show.inequality.warning")) {
      message("For consistency with the rest of the package the ",
              "inequality sign may be switched from >= to <= in a ",
              "future nloptr version.")
    }

    .hin <- match.fun(hin)
    hin <- function(x) -.hin(x)      # change  hin >= 0  to  hin <= 0 !
    if (is.null(hinjac)) {
      hinjac <- function(x) nl.jacobian(x, hin)
    } else {
      .hinjac <- match.fun(hinjac)
      hinjac <- function(x) -.hinjac(x)
    }
  }

  S0 <- nloptr(x0,
               eval_f = fn,
               eval_grad_f = gr,
               lb = lower,
               ub = upper,
               eval_g_ineq = hin,
               eval_jac_g_ineq = hinjac,
               opts = opts)

  if (nl.info) print(S0)

  list(par = S0$solution, value = S0$objective, iter = S0$iterations,
       convergence = S0$status, message = S0$message)
}