Introduction to Optimization - Numerical Methods in Engineering with MATLAB - page 387

goldSearch

Thisfunction implements the golden section search algorithm.

function [xMin,fMin] = goldSearch(func,a,b,tol)
% Golden section search for the minimum of f(x).
%Theminimumpointmustbebracketedina<=x<=b.
% USAGE: [fMin,xMin] = goldSearch(func,xStart,h)
% INPUT:
% func = handle of function that returns f(x).

% a, b = limits of the interval containing the minimum.

% tol = error tolerance (default is 1.0e-6).

% OUTPUT:
% fMin = minimum value of f(x).
%xMin=valueofxattheminimumpoint.

if nargin < 4; tol = 1.0e-6; end
nIter = ceil(-2.078087*log(tol/abs(b-a)));
R = 0.618033989;
C=1.0-R;
% First telescoping
x1=R*a+C*b;
x2=C*a+R*b;
f1 = feval(func,x1);
f2 = feval(func,x2);
%Mainloop
for i =1:nIter
iff1>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