Add some notes in the docs about global minimization

[santosmv]

Hello,
I have looked at the documentation, but it was not so clear for me (as a beginner) whether iminuit MIGRAD is able to find a global minimum or a local one. If it finds the global minimum, could it be local any time?
Any clue will be very helpful.

Best regards

[HDembinski]

MIGRAD and any other hill-climbing algorithm only finds a local minimum. Where did you look for this information in the docs? I am happy to add a sentence there explaining this.

[santosmv]

Hi Hans,
Mainly in the Reference guide: https://iminuit.readthedocs.io/en/stable/reference.html
The migrad section directs us to Minuit paper, in which discusses about global minimum search, but has the iminuit the functionality to find the global minimum (described in the paper)?

Thanks!

[HDembinski]

Ok, I see now what you mean. No the "IMPROVE" algorithm is not implemented in MINUIT2 at all (only in original MINUIT in Fortran). The enthusiasm of the paper is misguided about this method. To me, it sounds like a terrible idea to find a global minimum. If you need global optimization, I would recommend to use one of the algorithms in libnlopt or scipy. Note that global optimization still has no unique solution. There is not one best algorithm for doing it. There are many heuristic algorithms out there. Generally there are no proofs that they find the global minimum in finite time or that one particular algorithm is faster than all the others. There are the no free lunch theorems which say that an algorithm with performs well in some class of problems must pay with worse performance in other classes of problems.

In practice, the algorithms in scipy and nlopt probably work ok. You can use one of those algorithms and then start Minuit with that solution.

[santosmv]

Got it. Thank you for the explanation, it was enlightening to me.