MATLAB: Setup fmincon with nonlinear constraint condition

Question

I am doing an optimisation job using fmincon with nonlinear constraint condition. I have tried several different input dataset, but always got message indicating local minimum possible. I then configured fmincon options with more stringent stopping criteria. Surely, the computation took longer time and output different result comparing with previous fmincon setup. However, it still suggests local minimum possible.

I've tried all three fmincon optimisation methods. It turns out they mostly output quite different results. And, the active-set method is pretty slow.

Question: 1. Any tip to setup fmincon in order to get more or less convergent results.

2. Any tip to speedup the computation? Actually my problem is not that high dimension (10), and input data is not that large (around 10k).

Thank you very much for your suggestions.

Mono

Answer 1

A local minimum is what fmincon is looking for. The message means it thinks it succeeded.

If you don't like the solution it found, it is possible that you need a better initial guess. That's a matter of art, I'm afraid.