GoldenSectionSearch

Finds the argument minimizing the function f in the interval [a,b] assuming f is unimodal on the interval, i.e. has only one local minimum and no local maximum. The maximum error in the result is eps. Works equally well for maximization with a small change in the code. See TernarySearch.h in the Various chapter for a discrete version.

Time: O(log((b-a) / ε)) 14 lines tested

Usage: double func(double x) return 4+x+.3*x*x; double xmin = gss(-1000,1000,func);

content/numerical/GoldenSectionSearch.h — Ulf Lundstrom, source: Numeriska algoritmer med matlab, Gerd Eriksson, NADA, KTH

double gss(double a, double b, double (*f)(double)) {
	double r = (sqrt(5)-1)/2, eps = 1e-7;
	double x1 = b - r*(b-a), x2 = a + r*(b-a);
	double f1 = f(x1), f2 = f(x2);
	while (b-a > eps)
		if (f1 < f2) { //change to > to find maximum
			b = x2; x2 = x1; f2 = f1;
			x1 = b - r*(b-a); f1 = f(x1);
		} else {
			a = x1; x1 = x2; f1 = f2;
			x2 = a + r*(b-a); f2 = f(x2);
		}
	return a;
}