inst/tinytest/test-hs023.R

In nloptr: R Interface to NLopt

# Copyright (C) 2010 Jelmer Ypma. All Rights Reserved.
# SPDX-License-Identifier: LGPL-3.0-or-later
#
# File:   test-hs023.R
# Author: Jelmer Ypma
# Date:   16 August 2010
#
# Maintenance assumed by Avraham Adler (AA) on 2023-02-10
#
# Example problem, number 23 from the Hock-Schittkowsky test suite..
#
# \min_{x} x1^2 + x2^2
# s.t.
#   x1 + x2 >= 1
#   x1^2 + x2^2 >= 1
#   9*x1^2 + x2^2 >= 9
#   x1^2 - x2 >= 0
#   x2^2 - x1 >= 0
#
# with bounds on the variables
#   -50 <= x1, x2 <= 50
#
# we re-write the inequalities as
#   1 - x1 - x2 <= 0
#   1 - x1^2 - x2^2 <= 0
#   9 - 9*x1^2 - x2^2 <= 0
#   x2 - x1^2 <= 0
#   x1 - x2^2 <= 0
#
# the initial value is
# x0 = (3, 1)
#
# Optimal solution = (1, 1)
#
# CHANGELOG:
#   2014-05-05: Changed example to use unit testing framework testthat.
#   2019-12-12: Corrected warnings and using updated testtthat framework (AA)
#   2023-02-07: Remove wrapping tests in "test_that" to reduce duplication. (AA)
#

library(nloptr)

# f(x) = x1^2 + x2^2
eval_f <- function(x) {
  list("objective" = x[1] ^ 2 + x[2] ^ 2,
       "gradient" = c(2 * x[1], 2 * x[2]))
}

# Inequality constraints.
eval_g_ineq <- function(x) {
  constr <- c(1 - x[1] - x[2],
              1 - x[1] ^ 2 - x[2] ^ 2,
              9 - 9 * x[1] ^ 2 - x[2] ^ 2,
              x[2] - x[1] ^ 2,
              x[1] - x[2] ^ 2)
  grad <- rbind(c(-1, -1),
                c(-2 * x[1], -2 * x[2]),
                c(-18 * x[1], -2 * x[2]),
                c(-2 * x[1], 1),
                c(1, -2 * x[2]))
  list("constraints" = constr, "jacobian" = grad)
}

# Initial values.
x0 <- c(3, 1)

# Lower and upper bounds of control.
lb <- c(-50, -50)
ub <- c(50,  50)

# Optimal solution.
solution.opt <- c(1, 1)

# Solve with MMA.
opts <- list("algorithm"            = "NLOPT_LD_MMA",
             "xtol_rel"             = 1.0e-6,
             "tol_constraints_ineq" = rep(1.0e-6, 5),
             "print_level"          = 0)

res <- nloptr(
  x0          = x0,
  eval_f      = eval_f,
  lb          = lb,
  ub          = ub,
  eval_g_ineq = eval_g_ineq,
  opts        = opts
)

# Run some checks on the optimal solution.
expect_equal(res$solution, solution.opt, tolerance = 1e-6)
expect_true(all(res$solution >= lb))
expect_true(all(res$solution <= ub))

# Check whether constraints are violated (up to specified tolerance).
expect_true(
  all(eval_g_ineq(res$solution)$constr <= res$options$tol_constraints_ineq)
)