Optimization: Himmelblau’s Function

I just came across Himmelblau’s function for testing optimization routines. It has four local minima and one maxima so it provides a good test:

I’m pleased to say my implementation of the Nelder-Meade Simplex Algorithm (on my C++ page here) was able to optimize it for each minima (depending on the starting locations of course). I did have a weird problem though – starting a solution at (0,0) failed, even though the minima are not equidistant from the origin. Go figure!