optimization procedure convergence and "norm of step"

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Matthew on 18 Sep 2014
Answered: Alan Weiss on 22 Sep 2014
I am trying to solve an optimization problem with fmincon. Unfortunately, the optimization runs forever. When I turned on "Iterative Display", I noticed that "norm of step" becomes very tiny and seems to oscillate (see example output below).
I interpret this small "norm step" to mean that I can safely assume the optimization procedure has in fact converged (even if the solver does not think so).
Is this assumption valid?
(Note that I am using the fmincon default x-tolerance of 1e-10. This would explain why the procedure is failing to converge, even with a norm-step of 1e-08.)
Example output from my fmincon optimization procedure:
First-order Norm of
Iter F-count f(x) Feasibility optimality step
4449 5268 4.051585e+07 0.000e+00 5.432e+09 1.160e-08
4450 5269 4.051585e+07 0.000e+00 5.432e+09 1.156e-08
4451 5270 4.051585e+07 0.000e+00 5.432e+09 1.160e-08
4452 5271 4.051585e+07 0.000e+00 5.432e+09 1.156e-08
4453 5272 4.051585e+07 0.000e+00 5.432e+09 1.160e-08
4454 5273 4.051585e+07 0.000e+00 5.432e+09 1.156e-08
4455 5274 4.051585e+07 0.000e+00 5.432e+09 1.160e-08
4456 5275 4.051585e+07 0.000e+00 5.432e+09 1.156e-08
4457 5276 4.051585e+07 0.000e+00 5.432e+09 1.160e-08
4458 5277 4.051585e+07 0.000e+00 5.432e+09 1.156e-08
4459 5278 4.051585e+07 0.000e+00 5.432e+09 1.160e-08
4460 5279 4.051585e+07 0.000e+00 5.432e+09 1.156e-08
4461 5280 4.051585e+07 0.000e+00 5.432e+09 1.160e-08

1 Comment

Matt J on 19 Sep 2014
Is this assumption valid?
No, you cannot assume that. We need to see the code that you ran.