fmincon message: first order oplimality not below the tollerance but all constraints are satisfied. How to interpret this message?

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Dear all matlab community. I'm running an optimal power flow using fmincon with sqp algorithm. My question concerns the outcome message given by fmincon at the end of the optimization. Maybe it could be useful to say that i'm not furnishing any gradient and Hessian to the function.
The message shown is: Optimization stopped because the relative changes in all elements of x are less than options.TolX = 1.000000e-14, and the relative maximum constraint violation, 1.618573e-08, is less than options.TolCon = 1.000000e-06. The first order optimality is not under the fixed tollerance of 10^-6.
How do I have to interpret this message? My guess is: The solution in not the optimal one but being all the constraints satisfied, it is still feasible and acceptable. For sure that involves to bear in mind, the achieved solution is not the optimal.
Is my guess right? or do i have to consider the reached solution complitely not valid!?
Thanks to all in advance.

Answers (1)

Alan Weiss
Alan Weiss on 1 Aug 2014
Take a look at the Local Minimum Possible section of the documentation.
It is not clear to me whether you understand the difference between a local solution and a global solution. fmincon attempts to produce a local solution, it makes no claim about producing a global solution.
I hope that this helps.
Alan Weiss
MATLAB mathematical toolbox documentation

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