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Subject: Re: Computational complexity of fmincon algorithm
Date: Sun, 8 Nov 2009 16:05:19 +0000 (UTC)
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"Lior Vernia" <liorvern@post.tau.ac.il> wrote in message <hd4jva$gd$1@fred.mathworks.com>...
Obviously fmincon is the one who decides how many times to compute f(x), and its gradients and Hessian, so how does that depend on n?
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Well, the number of times it computes f() and its derivatives depends on how many iterations it needs to reach some stopping/convergence criterion. So, the complexity I guess is O(N*T(n)) where N is the number of iterations it ends up running.

The number of iterations though is influenced in part by you, since you choose the stopping/convergence criteria through optional arguments passed to fmincon. It obviously also depends on the shape of the graph of f(), e.g. the condition number of the Hessian at the solution. Some functions just take more iterations to minimize than others.