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# Copyright (C) 2014 Hans W. Borchers. All Rights Reserved.
# SPDX-License-Identifier: LGPL-3.0-or-later
#
# File: lbfgs.R
# Author: Hans W. Borchers
# Date: 27 January 2014
#
# Wrapper to solve optimization problem using Low-storage BFGS.
#
# CHANGELOG
#
# 2023-02-09: Cleanup and tweaks for safety and efficiency (Avraham Adler)
#
#' Low-storage BFGS
#'
#' Low-storage version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.
#'
#' The low-storage (or limited-memory) algorithm is a member of the class of
#' quasi-Newton optimization methods. It is well suited for optimization
#' problems with a large number of variables.
#'
#' One parameter of this algorithm is the number \code{m} of gradients to
#' remember from previous optimization steps. NLopt sets \code{m} to a
#' heuristic value by default. It can be changed by the NLopt function
#' \code{set_vector_storage}.
#'
#' @param x0 initial point for searching the optimum.
#' @param fn objective function to be minimized.
#' @param gr gradient of function \code{fn}; will be calculated numerically if
#' not specified.
#' @param lower,upper lower and upper bound constraints.
#' @param nl.info logical; shall the original NLopt info been shown.
#' @param control list of control parameters, see \code{nl.opts} for help.
#' @param ... further arguments to be passed to the function.
#'
#' @return List with components:
#' \item{par}{the optimal solution found so far.}
#' \item{value}{the function value corresponding to \code{par}.}
#' \item{iter}{number of (outer) iterations, see \code{maxeval}.}
#' \item{convergence}{integer code indicating successful completion (> 0)
#' or a possible error number (< 0).}
#' \item{message}{character string produced by NLopt and giving additional
#' information.}
#'
#' @export lbfgs
#'
#' @author Hans W. Borchers
#'
#' @note Based on a Fortran implementation of the low-storage BFGS algorithm
#' written by L. Luksan, and posted under the GNU LGPL license.
#'
#' @seealso \code{\link{optim}}
#'
#' @references J. Nocedal, ``Updating quasi-Newton matrices with limited
#' storage,'' Math. Comput. 35, 773-782 (1980).
#'
#' D. C. Liu and J. Nocedal, ``On the limited memory BFGS method for large
#' scale optimization,'' Math. Programming 45, p. 503-528 (1989).
#'
#' @examples
#'
#' flb <- function(x) {
#' p <- length(x)
#' sum(c(1, rep(4, p-1)) * (x - c(1, x[-p])^2)^2)
#' }
#' # 25-dimensional box constrained: par[24] is *not* at the boundary
#' S <- lbfgs(rep(3, 25), flb, lower=rep(2, 25), upper=rep(4, 25),
#' nl.info = TRUE, control = list(xtol_rel=1e-8))
#' ## Optimal value of objective function: 368.105912874334
#' ## Optimal value of controls: 2 ... 2 2.109093 4
#'
lbfgs <- function(x0, fn, gr = NULL, lower = NULL, upper = NULL,
nl.info = FALSE, control = list(), ...) {
opts <- nl.opts(control)
opts["algorithm"] <- "NLOPT_LD_LBFGS"
fun <- match.fun(fn)
fn <- function(x) fun(x, ...)
if (is.null(gr)) {
gr <- function(x) nl.grad(x, fn)
} else {
.gr <- match.fun(gr)
gr <- function(x) .gr(x, ...)
}
S0 <- nloptr(x0,
eval_f = fn,
eval_grad_f = gr,
lb = lower,
ub = upper,
opts = opts)
if (nl.info) print(S0)
list(par = S0$solution, value = S0$objective, iter = S0$iterations,
convergence = S0$status, message = S0$message)
}
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