Nonlinear optimization problem: The final point is the initial point.

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Hi there
I am trying to perform a non-linear optimization of a model (non-linear line with 3 input parameters) to a positive intensity map, to obtain the line for which the highest total intensity is reached (i.e.: best line fit to the intensity map). The problem works well using fminsearch but I would like to constrain one of the parameters to positive values only and thus started looking into fmincon. Here the problem fails to converge on the following grounds:
Optimization completed: The final point is the initial point.
The first-order optimality measure, 0.000000e+00, is less than
options.TolFun = 1.000000e-06.
Optimization Metric Options
relative first-order optimality = 0.00e+00 TolFun = 1e-06 (default)
I have tried looking into the list of recommendations given at the top here but am unable to find a solution.
Does anyone have any suggestions to me? I have tried running the problem unconstrained with fminunc, suspecting that it might at least yield the same solution as fminsearch, but it too suggests to use the starting point. What am I doing wrong?

Accepted Answer

Alan Weiss
Alan Weiss on 11 Mar 2014
Most likely, you have finite difference steps that are too small. This section of the documentation describes the problem and possible solutions.
You might also be interested in using John D'Errico's fminsearchbnd, which uses clever nonlinear transformations to allow fminsearch to satisfy bounds.
Alan Weiss
MATLAB mathematical toolbox documentation
  1 Comment
Jakob Sievers
Jakob Sievers on 11 Mar 2014
Thank you very much for this suggestion Alan. The fminsearchbnd resolved the problem very nicely! Cheers!

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