fmincon: interior-point & SQP computational complexity
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Hi! I have a very lage-scale optimization problem and I need to know the computational complexity of the interior-point algorithm as well as SQP so that I can estimate, roughly, the computational time of a given computer or cluster.
Thanks to all in advance!
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Alan Weiss
le 11 Mar 2019
This question can probably be best estimated by scaling the problem from small to medium to lmedium-arge, running fmincon on all scales, and extrapolating, rather than by doing a theoretical computation. It matters very much what kinds of constraints you have (bounds, linear, nonlinear), and whether constraint matrices are sparse or not.
As explained here, there can be large differences in performance between the interior-point algorithm (which is large-scale) and the sqp algorithm (which is not large-scale). See fmincon Algorithms.
The algorithm descriptions can be found in Constrained Nonlinear Optimization Algorithms, but I think that you would have to work pretty hard to get the complexity estimates out of those descriptions. Sorry, I don't know anything else.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation
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Carlo Cavicchia
le 2 Mai 2019
Hi, thanks for the information! Can you share with us the references of the computational complexity of SQP?
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