Usually, the more you know about the function (gradients, Hessians, etc.) and higher order optimization technique is used (Interpolation methods, Quasi-Newton > Newton's method) > the less function evaluation is needed to find an optimum.
Let's say I have a function that is very costly to calculate.
What technique should be used to find an optimum with as less function evaluation as possible?
Is there any chart of the internet to compare different optimization methods in term of "# of the objective function evaluation" vs "the complexity & cost of intermediate steps"?