When does fmincon's interior-point algorithm accept a larger function value while searching for the optimum?

Hello,

I am currently using fmincon's interior-point algorithm to solve a minimization problem. There isn't an analytical gradient I can provide to fmincon. I have turned on the display for each iteration and have seen that the f(x) column increases with each iteration, even when the previous f(x) was evaluated at a feasible point (the feasibility column displays a 0).

I just want to understand the possible reasons for this behavior. Shouldn't fmincon never accept points that do not improve on the previous iteration, given that the previous point was feasible? Could it be because of the gradient fmincon computes numerically?

Thank you for your time.

Answer 1

[Alan Weiss]

You can see the interior-point algorithm description. There is no requirement in the algorithm that the objective function decrease at each iteration. There could be many reasons that the objective function initially increases, or even increases at random-seeming iterations. However, if the eventual answer that fmincon returns is higher than intermediate answers, then perhaps you can try using a different algorithm (I would first try 'sqp') or try setting the InitBarrierParam option to a larger-than-default value such as 100 or 1000, or set the ScaleProblem option to true.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Suraj Upadhyay]

Thank you for the answer! You even seemed to preempt my follow-up question (what to do if my answer lead to a function value greater than at some intermediate step). In some cases, I'm seeing that the answer's actually worse than my starting values! I'll definitely implement what you recommended.

Thanks a ton!