2D Minimization problem, not good for fminsearch?

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Allen Goldstein
Allen Goldstein on 18 Oct 2021
Answered: Bjorn Gustavsson on 19 Oct 2021
My 2D objective function is like finding a whirlpool in the surface of a lake. I do not have good initial guesses. Below example is in the middle of the surface but it may be anywhere on the surface and the diamerter may be smaller than shown in the example.
I was thinking that fminsearch would work but if the initial guess is on the flat surface, it will go a short distance then stop (shown by the dots on the left which increase in size as iteration count goes up.).
I was thinking that if I could increase the multiplier of the search (1.05 by default), I could better set up the problem with an initial guess in the center of the surface and a large spread of the trial points. But I find that there is no option to change the multiplier used in fminsearch.
Does anyone have a suggestion for how to better approach this minimization problem in MATLAB?

Answers (1)

Bjorn Gustavsson
Bjorn Gustavsson on 19 Oct 2021
For problems like these (It seems likely that your function has multiple local minima or at least very very flat regions) the best choise might be to use multiple starting-points in some "region of expected dominant minima" to get fminsearch to find the minima. The spacing between the start-guess should be reasonable to figure out from what you know/expect from the "FWHm" of the minima - you'll only need one start-guess in that region (from your figure something like 4x4 start-guesses ought to be enough to find this.).
HTH

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