unc_n2_goldstein.m

matlab最优化理论的实现

function [f]=unc_n2_goldstein(x)
%reference:
%note that you can get the formulation of unc_n2_goldstein from some
%aritcles,such as
%(1)LS Zhang, CK Ng, D Li, WW Tian  'A New Filled Function Method for Global Optimization',
%Journal of Global Optimization,Problem 5 (Goldstein and Price function )
%
%algorithm:
%below code is  edited according to 
%(1)LS Zhang, CK Ng, D Li, WW Tian  'A New Filled Function Method for Global Optimization',
%Journal of Global Optimization,Problem 5 (Goldstein and Price function )
%
% solution:
% where the bounds are -3<=x1,x2<=3;
% The global minimum is at x*=(0,-1)  and f(x*)= 3;

%Copyright:
% programmers:oiltowater.
% It comply with the GPL2.0
% Copyright 2006  oiltowater 

x1=x(1,1);
x2=x(2,1);
g=1+(x1+x2+1).^2*(19-14*x1+3*x1.^2-14*x2+6*x1*x2+3*x2.^2);
h=30+(2*x1-3*x2).^2*(18-32*x1+12*x1^2+48*x2-36*x1*x2+27*x2.^2);
f=g*h;