R/mma.R

In 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)
# 2024-06-04: Switched desired direction of the hin/hinjac inequalities, leaving
#       the old behavior as the default for now. Also cleaned up the HS100
#       example. (Avraham Adler)
#

#' Method of Moving Asymptotes
#'
#' Globally-convergent method-of-moving-asymptotes (\acronym{MMA}) algorithm for
#' gradient-based local optimization, including nonlinear inequality
#' constraints (but not equality constraints).
#'
#' This is an improved \acronym{CCSA} ("conservative convex separable
#' approximation") variant of the original \acronym{MMA} algorithm published by
#' Svanberg in 1987, which has become popular for topology optimization.
#'
#' @param x0 starting point for searching the optimum.
#' @param fn objective function that is to be minimized.
#' @param gr gradient of function \code{fn}; will be calculated numerically if
#' not specified.
#' @param lower,upper lower and upper bound constraints.
#' @param hin function defining the inequality constraints, that is
#' \code{hin <= 0} for all components.
#' @param hinjac Jacobian of function \code{hin}; will be calculated
#' numerically if not specified.
#' @param nl.info logical; shall the original NLopt info been shown.
#' @param control list of options, see \code{nl.opts} for help.
#' @param deprecatedBehavior logical; if \code{TRUE} (default for now), the old
#' behavior of the Jacobian function is used, where the equality is \eqn{\ge 0}
#' instead of \eqn{\le 0}. This will be reversed in a future release and
#' eventually removed.
#' @param ... additional arguments passed to the function.
#'
#' @return List with components:
#'   \item{par}{the optimal solution found so far.}
#'   \item{value}{the function value corresponding to \code{par}.}
#'   \item{iter}{number of (outer) iterations, see \code{maxeval}.}
#'   \item{convergence}{integer code indicating successful completion (> 1)
#'   or a possible error number (< 0).}
#'   \item{message}{character string produced by NLopt and giving additional
#'   information.}
#'
#' @export mma
#'
#' @author Hans W. Borchers
#'
#' @note \dQuote{Globally convergent} does not mean that this algorithm
#'   converges to the global optimum; rather, it means that the algorithm is
#'   guaranteed to converge to some local minimum from any feasible starting
#'   point.
#'
#' @seealso \code{\link{slsqp}}
#'
#' @references Krister Svanberg, \dQuote{A class of globally convergent
#'   optimization methods based on conservative convex separable
#'   approximations}, SIAM J. Optim. 12 (2), p. 555-573 (2002).
#'
#' @examples
#'
#' #  Solve the Hock-Schittkowski problem no. 100 with analytic gradients
#' #  See https://apmonitor.com/wiki/uploads/Apps/hs100.apm
#'
#' x0.hs100 <- c(1, 2, 0, 4, 0, 1, 1)
#' fn.hs100 <- function(x) {(x[1] - 10) ^ 2 + 5 * (x[2] - 12) ^ 2 + x[3] ^ 4 +
#'                          3 * (x[4] - 11) ^ 2 + 10 * x[5] ^ 6 + 7 * x[6] ^ 2 +
#'                          x[7] ^ 4 - 4 * x[6] * x[7] - 10 * x[6] - 8 * x[7]}
#'
#' hin.hs100 <- function(x) {c(
#' 2 * x[1] ^ 2 + 3 * x[2] ^ 4 + x[3] + 4 * x[4] ^ 2 + 5 * x[5] - 127,
#' 7 * x[1] + 3 * x[2] + 10 * x[3] ^ 2 + x[4] - x[5] - 282,
#' 23 * x[1] + x[2] ^ 2 + 6 * x[6] ^ 2 - 8 * x[7] - 196,
#' 4 * x[1] ^ 2 + x[2] ^ 2 - 3 * x[1] * x[2] + 2 * x[3] ^ 2 + 5 * x[6] -
#'  11 * x[7])
#' }
#'
#' gr.hs100 <- function(x) {
#'  c( 2 * x[1] - 20,
#'    10 * x[2] - 120,
#'     4 * x[3] ^ 3,
#'     6 * x[4] - 66,
#'    60 * x[5] ^ 5,
#'    14 * x[6] - 4 * x[7] - 10,
#'     4 * x[7] ^ 3 - 4 * x[6] - 8)
#' }
#'
#' hinjac.hs100 <- function(x) {
#'   matrix(c(4 * x[1], 12 * x[2] ^ 3, 1, 8 * x[4], 5, 0, 0,
#'            7, 3, 20 * x[3], 1, -1, 0, 0,
#'            23, 2 * x[2], 0, 0, 0, 12 * x[6], -8,
#'            8 * x[1] - 3 * x[2], 2 * x[2] - 3 * x[1], 4 * x[3], 0, 0, 5, -11),
#'            nrow = 4, byrow = TRUE)
#' }
#'
#' #  The optimum value of the objective function should be 680.6300573
#' #  A suitable parameter vector is roughly
#' #  (2.330, 1.9514, -0.4775, 4.3657, -0.6245, 1.0381, 1.5942)
#'
#' # Using analytic Jacobian
#' S <- mma(x0.hs100, fn.hs100, gr = gr.hs100,
#'       hin = hin.hs100, hinjac = hinjac.hs100,
#'       nl.info = TRUE, control = list(xtol_rel = 1e-8),
#'       deprecatedBehavior = FALSE)
#'
#' # Using computed Jacobian
#' S <- mma(x0.hs100, fn.hs100, hin = hin.hs100,
#'       nl.info = TRUE, control = list(xtol_rel = 1e-8),
#'       deprecatedBehavior = FALSE)
#'

mma <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL, hin = NULL,
                hinjac = NULL, nl.info = FALSE, control = list(),
                deprecatedBehavior = TRUE, ...) {

  opts <- nl.opts(control)
  opts["algorithm"] <- "NLOPT_LD_MMA"

  fun <- match.fun(fn)
  fn  <- function(x) fun(x, ...)

  if (is.null(gr)) {
    gr <- function(x) nl.grad(x, fn)
  } else {
    .gr <- match.fun(gr)
    gr <- function(x) .gr(x, ...)
  }


  if (!is.null(hin)) {
    if (deprecatedBehavior) {
      warning("The old behavior for hin >= 0 has been deprecated. Please ",
              "restate the inequality to be <=0. The ability to use the old ",
              "behavior will be removed in a future release.")
      .hin <- match.fun(hin)
      hin <- function(x) -.hin(x, ...)      # change  hin >= 0  to  hin <= 0 !
    }
    if (is.null(hinjac)) {
      hinjac <- function(x) nl.jacobian(x, hin)
    } else if (deprecatedBehavior) {
      warning("The old behavior for hinjac >= 0 has been deprecated. Please ",
              "restate the inequality to be <=0. The ability to use the old ",
              "behavior will be removed in a future release.")
      .hinjac <- match.fun(hinjac)
      hinjac <- function(x) -.hinjac(x)
    }
  }

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

  if (nl.info) print(S0)

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