I'm attempting derivative-free minimization of, essentially, a black-box function in one dimension. Up to now I've been using BOBYQA as implemented in NLopt. The shape of the function looks like this:
Clearly, giving a good initial guess will help immensely here, as I can avoid the nasty flat region to the right of the graph. However, sometimes a good initial guess is unavailable, and it can end up in the flat region and hence never find the minima.
- Are there any tips/tricks for getting out/avoiding the flat region at all?
- Would a simple Fibonacci / Golden Section search be any better?
- Or would my time be better spent on working out good initial guesses?