% Six-Hump camel back function L. LAURENT -- 13/12/2010 -- luc.laurent@lecnam.net
0001 %% Six-Hump camel back 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 %6 local minima and 2 global: 0026 %f(x1,x2)=-1.0316 for (x1,x2)={(-0.0898,0.7126),(0.0898,0.7126)} 0027 % 0028 %Design space: -3<x1<3 -2<x2<2 0029 %(recommanded: -2<x1<2 -1<x2<1) 0030 0031 function [p,dp]=funCamelbackSixHump(xx) 0032 0033 %constants 0034 a=4; 0035 b=2.1; 0036 c=3; 0037 0038 %variables 0039 xxx=xx(:,:,1); 0040 yyy=xx(:,:,2); 0041 0042 %evaluations and derivatives 0043 pa=(a-b*xxx.^2+xxx.^4/c); 0044 pb=(-1+yyy.^2); 0045 p=pa.*xxx.^2+... 0046 xxx.*yyy... 0047 +a*pb.*yyy.^2; 0048 0049 if nargout==2 0050 dp(:,:,1)=2*xxx.*pa... 0051 +xxx.^2.*(-2*b*xxx+a*xxx.^3/c)... 0052 +yyy; 0053 dp(:,:,2)=xxx... 0054 +2*a*yyy.*pb... 0055 +2*a*yyy.^3; 0056 end 0057 end