I read some topics in this forum about calibration and minimization. It seems that when the situation becomes difficult, the best way to act is to start with a global minimization algorithm and then moveto a local minimization algorithm in order to speed up the search. How should one choose when switching from an algorithm to another? Better, how is one sure that he reached a neighborhood of theglobal minimum?

i guees it depends whether you talk about deterministic or heuristic optimization, the initial conditions, and what you are actually try to find.

My problem is just to find the global minimum of a function, the behavior of which is difficult to guess. A global minimization algorithm would probably give me the real minimum, but it is known that this approach is much slower when compared to local algorithms that on the other hand could return a local minimum and not the global one. That's why the combination of the two approaches could be the best solution. My problem is that I don't know how to combine them

there's no magic, my friend. you can't find the global minimum in general case. you need some knowledge about minimums, like the number of them or maybe proximity to each other. otherwise, all you can do is do the grid, and in each point go Newton-Raphson. you could do the random grid too.

I remember having tried Ingber's ASA algorithm. I think it already does the optimization and switching between local/global modes. eg., when I tried minimizing a function with a single minima the convergence was very fast and as good as levenberg or other algorithms.While when I tried doing it for Heston model calibration it took many hours, and the resulting value kept changing depending on input parameter for maximum number of trials.

try a simulated annealing method. At least in theory it converges to global minimum with prob 1.have a look at numerical recipes for a detailled description. I have good experiences with that approach for different models (hull white 1F, 2F, stoch vol (heston type) libor market model).

To answer your question about when to switch from slow-but-global to fast-but-local: I have not seen any discussion in the literature beyond "use common sense". I would say to formulate some criterion in terms of the same primitives used to build convergence criterion. When the diameter of the subspace is some multiple of the whole search space, say, or when the slow-but-global slows down too much.

simulated annealing must be callibrated too .

QuoteOriginally posted by: shabani40My problem is just to find the global minimum of a function, the behavior of which is difficult to guess. A global minimization algorithm would probably give me the real minimum, but it is known that this approach is much slower when compared to local algorithms that on the other hand could return a local minimum and not the global one. That's why the combination of the two approaches could be the best solution. My problem is that I don't know how to combine themYou can use genetic method (DESolver) to find the global minimum and then use Levenberg-Marquardt for a local minimum.Good luck