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 atall?Would a simple Fibonacci / Golden Section search be any better?Or would my time be better spent on working out good initial guesses?
Derivative-free optimization of function with a flat region
optimization
The following works in any dimension:If you have a poor initial guess $x_0$ only (but outside the completely flat region), minimize $f(x)+c_k||x-x_k||^2$ for $k=0$ with some small $c_0$, call the result $x_1$, and iterate with a strongly decreasing sequence of $c_k$'s. In many cases $c_1=0$ will already work.