golden.m~

optimization using golden section search

%xmin - returns this
%fxmin - this
%n - and this
function[xmin,fxmin,n] = golden (xl,xu,maxit,tol,g)

% xl = 0.5;
% xu = 2;
% maxit = 100;
% tol = 0.001;
% f= x^3 - 2*sin(x);

R = (5^0.5 - 1)/2;
d = R.* (xu - xl);
x1 = xl + d;
x2 = xu - d;
f1 = feval(g,x1);
f2 = feval(g,x2);

if f1 > f2
    xopt = x1;
    fx = f1;
else
    xopt = x2;
    fx = f2;
end
while (ea > tol & n<maxit)
    d = R*d;
    if f1 > f2
        xl = x2;
        x2 = x1;
        x1 = xl + d;
        f2 = f1;
        f1 = feval(g,x1);
    else 
        xu = x1;
        x1 = x2;
        x2 = xu - d;
        f1 = f2;
        f2 = f);
    end
    n = n +1;
    if f1 > f2
        xopt = x1;
        fx = f1;
    else
        xopt = x2;
        fx = f2;
    end
    if xopt ~= 0;
        ea = (1.-R)*abs((xu-xl)/xopt)*100;
    end
end
xmin = xopt;
fxmin = fx;