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% STK_TESTFUN_GOLDSTEINPRICE computes the Goldstein-Price function
%
% The Goldstein-Price function [1] is a classical test function for
% global optimization algorithms, which belongs to the well-known
% Dixon-Szego test set [2].
%
% It is usually minimized over [-2; 2] x [-2; 2]. It has a unique
% global minimum at x = [0, -1] with f(x) = 3, and several local minima.
%
% REFERENCES
%
% [1] Goldstein, A.A. and Price, I.F. (1971), On descent from local
% minima. Mathematics of Computation, 25(115).
%
% [2] Dixon L.C.W., Szego G.P. (1978), Towards Global Optimization 2,
% North-Holland, Amsterdam, The Netherlands
% Copyright Notice
%
% Copyright (C) 2014 SUPELEC
%
% Author: Julien Bect <julien.bect@centralesupelec.fr>
%
% Based on the "Virtual Library for Simulation Experiments"
% Copyright (C) 2013 Derek Bingham, Simon Fraser University
% Authors: Sonja Surjanovic & Derek Bingham (dbingham@stat.sfu.ca)
% Distributed under the GPLv2 licence
% http://www.sfu.ca/~ssurjano/Code/goldprm.html
% Copying Permission Statement
%
% This file is part of
%
% STK: a Small (Matlab/Octave) Toolbox for Kriging
% (https://github.com/stk-kriging/stk/)
%
% STK is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free
% Software Foundation, either version 3 of the License, or (at your
% option) any later version.
%
% STK 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 General Public
% License for more details.
%
% You should have received a copy of the GNU General Public License
% along with STK. If not, see <http://www.gnu.org/licenses/>.
function y = stk_testfun_goldsteinprice (x)
if nargin == 0,
visu_goldsteinprice ();
return;
end
x = double (x);
x1 = x(:, 1);
x2 = x(:, 2);
x1x1 = x1 .^ 2;
x2x2 = x2 .^ 2;
x1x2 = x1 .* x2;
A1 = (x1 + x2 + 1) .^ 2;
A2 = 19 - 14*x1 + 3*x1x1 - 14*x2 + 6*x1x2 + 3*x2x2;
A = 1 + A1 .* A2; % 4th degree polynomial
B1 = (2*x1 - 3*x2) .^ 2;
B2 = 18 - 32*x1 + 12*x1x1 + 48*x2 - 36*x1x2 + 27*x2x2;
B = 30 + B1 .* B2; % 4th degree polynomial
y = A .* B; % 8th degree polynomial
end % function
function visu_goldsteinprice ()
s = 'Goldstein-Price function'; stk_figure (s);
xt = stk_sampling_regulargrid (80^2, 2, [[-2; 2], [-2; 2]]);
xt.colnames = {'x_1', 'x_2'};
surf (xt, @stk_testfun_goldsteinprice);
hold on; plot3 (0, -1, 3, 'r.');
colorbar; stk_title (s);
end % function
%!test % Use with nargin == 0 for visualisation
%! stk_testfun_goldsteinprice (); close all;
%!assert (stk_isequal_tolabs ...
%! (stk_testfun_goldsteinprice ([0, -1]), 3.0, 1e-12))
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