Can one run fminsearch on grids?

I understand that fminsearch does the search on the real line. Can one run fminsearch on grids like 0:0.01:1?

[rubindan]

You mean a discrete optimization? See

https://www.mathworks.com/matlabcentral/answers/334289-how-can-i-perform-optimization-over-a-discrete-set-of-possible-values-in-matlab

Answer 1

[John D'Errico]

No. fminsearch presumes a continuously valued function, defined everywhere. You CANNOT use it to solve discrete problems. And even though your search is not on a set of integers, it is still discrete. At best, you could try to use it for a continuous version of your problem, and then round the result at the very end, if you insisted on using fminsearch.

Your choices in MATLAB are either intlinprog form the optimization toolbox, or GA from the global optimization toolbox.

Of course, intlinprog presumes the objective function is linear, as well as any constraints. And while it also constrains the variables then to be integers, you can always multiply by 0.01 in the problem.

Finally, in many problems, the simple answer is to just try to evaluate the objective function at all points in the discrete sample space, then choose the best. This works when the sample space is not too large.

[alpedhuez]

"just try to evaluate the objective function at all points in the discrete sample space, then choose the best. This works when the sample space is not too large."

What should one do if this "brute-force" is too costly?

[John D'Errico]

Re-read my answer. I said to use either GA or INTLINPROG.

Only use the brute force approach IF IT IS NOT TOO COSTLY. I said brute force "...works when the sample space is not too large."