MATLAB: Interior-point in fmincon without inequality constraints

choose algorithmconstraintsoptimizationOptimization Toolbox

Dear all,
The MATLAB documentation recommends the interior-point algorithm for fmincon above the other three possibilities.
I wonder: is this still true if my problem has only equality constraints? Without inequality constraints there is no "interior" of anything…
Regards Andreas

Best Answer

You're correct, without inequalities, the interior point algorithm is a fairly straightforward algorithm. In the case where your problem only has equalities, the trust-region-reflective algorithm can be advantageous. Note, however, that you must provide analytical derivatives in order to use it.
The interior-point algorithm implementation has other features that add robustness: e.g. Hessian approximation options, ability to effectively use sparsity in the problem, ability to work with ultra-large problems via CG solves, etc. Therefore, it's usually worth trying as a first step.
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