Introduction to Optimization - Numerical Methods in Engineering with MATLAB - page 386

which yields

ln( ε/ | b − a | ) ε

n = =− 2 . 078 087 ln (10.4)

| |

ln R b − a

goldBracket

Thisfunction contains the bracketing algorithm. For the factor that multiplies suc-
cessivesearch intervals we chose c = 1 + R .

function [a,b] = goldBracket(func,x1,h)
% Brackets the minimum point of f(x).
% USAGE: [a,b] = goldBracket(func,xStart,h)
% INPUT:
% func = handle of function that returns f(x).

% x1 = starting value of x.

% h = initial step size used in search.

% OUTPUT:
%a,b=limitsonxattheminimumpoint.

c = 1.618033989;
f1 = feval(func,x1);
x2 = x1 + h; f2 = feval(func,x2);
% Determine downhill direction & change sign of h if needed.
iff2>f1
h=-h;
x2 = x1 + h; f2 = feval(func,x2);
%Checkifminimumisbetweenx1-handx1+h
iff2>f1
a=x2;b=x1-h;return

end

end
% Search loop
fori=1:100
h=c*h;
x3 = x2 + h; f3 = feval(func,x3);
iff3>f2
a=x1;b=x3;return

end
x1=x2;f1=f2;x2=x3;f2=f3;

end
error('goldbracket did not find minimum')