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% STK_TESTFUN_HARTMAN3 computes the "Hartman3" function
%
% The Hartman3 function is a test function in dimension 3, which is
% part of the famous Dixon & Szego benchmark [1] in global optimization.
%
% It is usually minimized over [0, 1]^3.
%
% HISTORICAL REMARKS
%
% This function belongs to a general class of test functions
% introduced by Hartman [2], hence the name.
%
% The particular set of coefficients used in the definition of the
% "Hartman3" function, however, seems to have been introduced by [1].
%
% GLOBAL MINIMUM
%
% According to [5], the function has one global minimum at
%
% x = [0.1, 0.55592003, 0.85218259].
%
% The corresponding function value is:
%
% f(x) = -3.862634748621772.
%
% A slightly lower value is attained [4] at
%
% x = [0.114614 0.554649 0.852547].
%
% The corresponding function value is:
%
% f(x) = -3.862747199255087
%
% The exact global optimum does not appear to be known.
%
% REFERENCES
%
% [1] L. C. W. Dixon & G. P. Szego (1978). Towards Global
% Optimization 2, North-Holland, Amsterdam, The Netherlands
%
% [2] J. K. Hartman (1973). Some experiments in global optimization.
% Naval Research Logistics Quarterly, 20(3):569-576.
%
% [3] V. Picheny, T. Wagner & D. Ginsbourger (2013). A benchmark
% of kriging-based infill criteria for noisy optimization.
% Structural and Multidisciplinary Optimization, 48:607-626.
%
% [4] S. Surjanovic & D. Bingham. Virtual Library of Simulation
% Experiments: Test Functions and Datasets. Retrieved March 3,
% 2022, https://www.sfu.ca/~ssurjano/hart4.html.
%
% [5] O. Roustant, D. Ginsbourger & Y. Deville (2012).
% DiceKriging package, version 1.6.0 from 2021-02-23
% URL: https://cran.r-project.org/web/packages/DiceKriging/index.html
% Author
%
% Julien Bect <julien.bect@centralesupelec.fr>
% Copying Permission Statement (this file)
%
% To the extent possible under law, CentraleSupelec has waived all
% copyright and related or neighboring rights to
% stk_testfun_hartman3.m. This work is published from France.
%
% License: CC0 <http://creativecommons.org/publicdomain/zero/1.0/>
% Copying Permission Statement (STK toolbox as a whole)
%
% 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_hartman3 (x)
a = [ ...
[ 3.0 0.1 3.0 0.1]; ...
[ 10.0 10.0 10.0 10.0]; ...
[ 30.0 35.0 30.0 35.0]];
p = [ ...
[ 0.3689 0.4699 0.1091 0.03815]; ...
[ 0.1170 0.4387 0.8732 0.57430]; ...
[ 0.2673 0.7470 0.5547 0.88280]];
c = [1.0 1.2 3.0 3.2];
y = stk_testfun_hartman_generic (x, a, p, c);
end % function
%!test
%! x1 = [0.1, 0.55592003, 0.85218259];
%! y1 = -3.862634748621772;
%!
%! x2 = [0.114614 0.554649 0.852547];
%! y2 = -3.862747199255087;
%!
%! y = stk_testfun_hartman3 ([x1; x2]);
%! assert (stk_isequal_tolabs (y, [y1; y2], 1e-15))
|
