I need to find a global minimum of a function f(omega), where omega is 2-D variable, and f(omega) is a numerical function, which means given an omega, I can know the value of f(omega). So I can't use derivative of f, when I am using FindMinimum, I need to use two initial values just as the Wolfram document says:
FindMinimum[f, x, x0 , x1 ] searches for a local minimum in f using x0 and x1 as the first two values of x, avoiding the use of derivatives.
f is a function has multiple minima on the 2-D omega plane, when I am using FindMinimum, I don't expect it could find the global minima, but the result indicates it does find the global minima most of the time. So it confused me about what FindMinimum was doing, I expect it only finds the local minimum. Although it finds the global minima is good for me, but I want it to be a STABLE(not most of time, or just in this case) routine to find the global minima. So I need to know what FindMinimum is doing exactly.
Does anybody happen to know that?