Page 300 - MATLAB an introduction with applications

Optimization ——— 285

function [xMin,fMin] = goldSearch(func,a,b,tol)
% Golden section search method
% func = function that returns f(x)
% a, b = limits of the interval for the minimum
% tol = error tol = 1.0e–6
% fMin = min of f(x)
% xMin = x at min point
if nargin < 4; tol = 1.0e–6; end
nIter = ceil(–2.078087*log(tol/abs(b–a)));
R = 0.618033989;
C = 1.0 – R;
x1 = R*a + C*b;
x2 = C*a + R*b;
f1 = feval(func,x1);
f2 = feval(func,x2);
for i =1:nIter
if f1 > f2
a = x1; x1 = x2; f1 = f2;
x2 = C*a + R*b;
f2 = feval(func,x2);
else
b = x2; x2 = x1; f2 = f1;
x1 = R*a + C*b;
f1 = feval(func,x1);
end
end
if f1 < f2; fMin = f1; xMin = x1;
else; fMin = f2; xMin = x2;
end

Example E5.9: Minimize the following function f (x) by the penalty function method:
2
2
2
2
f (x) = [(x + 2) + 5(x – 2) ] [(x – 1.5) + 0.5(x – 0.5) ]
2
2
1
1
 −x  0 
 1  
0
 −x 2  

subject to   3 −x 1 x x + 4x 2 − 6 ≤ 0 
1 2

 2 +x 1 x 2 − 5  
0

 2  
  3 −x 1 4x 2 − 4x 2    0 . 