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### Whether a “8 Integer Solution” given by DICOPT is an optimal solution?

Posted: Sat May 12, 2018 3:10 am
I use DICOPT to solve an MINLP model and it gives model status 8 Integer Solution. Then, how can I know whether it is an globel optimal solution? In the log file, I reads ** Optimal solution. Reduced gradient less than tolerance. and --- DICOPT: Best integer solution found: 567403973.551187, then can I deduce that it is exactly an globel optimal solution?

### Re: Whether a “8 Integer Solution” given by DICOPT is an optimal solution?

Posted: Sat May 12, 2018 5:55 pm
It depends on if the problem is convex or non-convex. If the problem is convex, (considering a well-scaled, well-bounded model), using the "crossover" stop criterion should yield the global optimum. But, if the problem is non-convex this criterion can stop prematurely. If this is the case, the (heuristic) NLP worsening criterion is advised to be used, which of course doesn't GUARANTEE that the optimum is global. ( I'm just repeating some of https://www.gams.com/latest/docs/S_DICOPT.html )

From my experience, the most important considerations for DICOPT to work properly are modeling ones (good scaling, good bounding). Of course, you should always use a global solver (or whatever procedure) once to get the global optimum, use this to tweak DICOPT and then enjoy its improved performance.

Best
Claudio