MATLAB: Inconsistent data in fmincon output structure

constrained optimizationfminconMATLAB and Simulink Student Suite

I'm using FMINCON to solve a constrained optimization problem. When I examine the output structure generated by FMINCON, I get inconsistent results for the first-order optimality measure.
For example, when I look in output.message, I see
'Local minimum found that satisfies the constraints.
     Optimization completed because the objective function is non-decreasing in 
     feasible directions, to within the default value of the optimality tolerance,
     and constraints are satisfied to within the default value of the constraint tolerance.
     Stopping criteria details:
     Optimization completed: The relative first-order optimality measure, 9.417002e-07,
     is less than options.OptimalityTolerance = 1.000000e-06, and the relative maximum constraint
     violation, 1.110223e-16, is less than options.ConstraintTolerance = 1.000000e-06.
     Optimization Metric                                            Options
     relative first-order optimality =   9.42e-07       OptimalityTolerance =   1e-06 (default)
     relative max(constraint violation) =   1.11e-16    ConstraintTolerance =   1e-06 (default)'
This indicates a first-order optimality measure of 9.47e-07. However, if I look at output.firstorderopt, I see
>> out.firstorderopt
ans =
 8.7505e-06
Does anyone have any idea what's going on? The code that generates this is a little complicated to summarise here, but I can upload it somewhere if someone would like to take a closer look.

Best Answer

The key word is "relative." The relative first-order optimality measure is (usually) the ratio of the final to the initial measure. So the initial first-order optimality measure was probably around 10.
Alan Weiss
MATLAB mathematical toolbox documentation
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