optimization procedure convergence and "norm of step"

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

[Matt J]

Is this assumption valid?

No, you cannot assume that. We need to see the code that you ran.

Answer 1

[Alan Weiss]

Your problem seems to have stalled. You might want to use some of the suggestions in < Too Many Iterations or Function Evaluations>.

Alan Weiss

MATLAB mathematical toolbox documentation