optimization procedure convergence and "norm of step"

Question

Matthew am 18 Sep. 2014

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https://de.mathworks.com/matlabcentral/answers/155370-optimization-procedure-convergence-and-norm-of-step

Beantwortet: Alan Weiss am 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
  5268    4.051585e+07    0.000e+00    5.432e+09    1.160e-08
  5269    4.051585e+07    0.000e+00    5.432e+09    1.156e-08
  5270    4.051585e+07    0.000e+00    5.432e+09    1.160e-08
  5271    4.051585e+07    0.000e+00    5.432e+09    1.156e-08
  5272    4.051585e+07    0.000e+00    5.432e+09    1.160e-08
  5273    4.051585e+07    0.000e+00    5.432e+09    1.156e-08
  5274    4.051585e+07    0.000e+00    5.432e+09    1.160e-08
  5275    4.051585e+07    0.000e+00    5.432e+09    1.156e-08
  5276    4.051585e+07    0.000e+00    5.432e+09    1.160e-08
  5277    4.051585e+07    0.000e+00    5.432e+09    1.156e-08
  5278    4.051585e+07    0.000e+00    5.432e+09    1.160e-08
  5279    4.051585e+07    0.000e+00    5.432e+09    1.156e-08
  5280    4.051585e+07    0.000e+00    5.432e+09    1.160e-08