% Goldstein & Price function L. LAURENT -- 13/12/2010 -- luc.laurent@lecnam.net
0001 %% Goldstein & Price function 0002 %L. LAURENT -- 13/12/2010 -- luc.laurent@lecnam.net 0003 0004 % sources available here: 0005 % https://bitbucket.org/luclaurent/optigtest/ 0006 % https://github.com/luclaurent/optigtest/ 0007 0008 % optiGTest - set of testing functions A toolbox to easy manipulate functions. 0009 % Copyright (C) 2017 Luc LAURENT <luc.laurent@lecnam.net> 0010 % 0011 % This program is free software: you can redistribute it and/or modify 0012 % it under the terms of the GNU General Public License as published by 0013 % the Free Software Foundation, either version 3 of the License, or 0014 % (at your option) any later version. 0015 % 0016 % This program is distributed in the hope that it will be useful, 0017 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0018 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0019 % GNU General Public License for more details. 0020 % 0021 % You should have received a copy of the GNU General Public License 0022 % along with this program. If not, see <http://www.gnu.org/licenses/>. 0023 0024 % 0025 %global minimum : f(x1,x2)=3 for (x1,x2)=(0,-1) 0026 % 0027 %Design space: -2<x1<2, -2<x<2 0028 0029 0030 function [p,dp]=funGoldsteinPrice(xx) 0031 %constants 0032 a=1; 0033 b=19; 0034 c=14; 0035 d=3; 0036 e=6; 0037 f=3; 0038 g=30; 0039 h=2; 0040 k=18; 0041 l=32; 0042 m=12; 0043 n=48; 0044 o=36; 0045 pp=27; 0046 0047 %variables 0048 xxx=xx(:,:,1); 0049 yyy=xx(:,:,2); 0050 0051 %evaluation and derivatives 0052 qq=xxx+yyy+a; 0053 rr=b-c*xxx+d*xxx.^2-c*yyy+e*xxx.*yyy+f*yyy.^2; 0054 ss=h*xxx-f*yyy; 0055 tt=k-l*xxx+m*xxx.^2+n*yyy-o*xxx.*yyy+pp*yyy.^2; 0056 % 0057 a = a+qq.^2.*rr; 0058 b = g+ss.^2.*tt; 0059 p = a.*b; 0060 0061 if nargout==2 0062 dqqX=1; 0063 dqqY=1; 0064 drrX=-c+2*d*xxx+e*yyy; 0065 drrY=-c+e*xxx+2*f*yyy; 0066 dssX=h; 0067 dssY=-f; 0068 dttX=-l+2*m*xxx-o*yyy; 0069 dttY=n-o*xxx+2*pp*yyy; 0070 % 0071 dp(:,:,1)=(2*dqqX.*qq.*rr+qq.^2.*drrX).*b... 0072 +(2*dssX.*ss.*tt+ss.^2.*dttX).*a; 0073 dp(:,:,2)=(2*dqqY.*qq.*rr+qq.^2.*drrY).*b... 0074 +(2*dssY.*ss.*tt+ss.^2.*dttY).*a; 0075 end 0076 end