% Powell function L. LAURENT -- 23/03/2017 -- luc.laurent@lecnam.net
0001 %% Powell function 0002 %L. LAURENT -- 23/03/2017 -- 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(x)=0 for xi=0 0026 % 0027 %Design space: -4<xi<5 0028 % 0029 0030 function [p,dp]=funPowell(xx) 0031 %constants 0032 a=10; 0033 b=5; 0034 c=2; 0035 d=10; 0036 0037 %evaluation and derivatives 0038 x=xx(:,:,1); 0039 y=xx(:,:,2); 0040 z=xx(:,:,3); 0041 v=xx(:,:,4); 0042 % 0043 pa=z+a*x; 0044 pb=y-v; 0045 pc=x-c*y; 0046 pd=z-v; 0047 % 0048 p=sum(pa.^2+b*pb.^2+pc.^4+d*pd.^4,3); 0049 % 0050 if nargout==2 0051 % 0052 dp=zeros(size(xx)); 0053 % 0054 dp(:,:,1)=2*a*pa+4*pc.^3; 0055 dp(:,:,2)=2*b*pb-4*c*pc.^3; 0056 dp(:,:,3)=2*pa+4*d*pd.^3; 0057 dp(:,:,4)=-2*b*pb-4*d*pd.^3; 0058 end