What are some methods or approaches by which one can assess the quality of a MINLP problem?
If we let the solver solve the relaxed problem, do we get a useful lower bound ?
because, even if we relax the problem , the NLP part is non-convex, and probably a local optimum would be obtained.
So, does relaxation help to understand how good our MINLP solution is?
what are some better ways ?
You aren't sufficiently clear, I think.
Q1. What is the appearance of the MINLP in question?
Q2. Connected to Q1, how do you form the "relaxed problem"? You have to be more specific, as there are probably more than one possible relaxation. (MINLP could refer to a structured problem posed as a mixed-integer nonlinear program, and even that problem could have a variety of appearances, and hence a variety of approaches could be utilized. We need to know which.
Thanks for letting me know.
the problem is a MINLP problem with a non-convex equality constraint.
As of relaxation, since Im employing GAMS, I do not know exactly which relaxation scheme the solvers make use of.
My guess is that there is an SQP-type solver underneath, with some additional strategies built in to control penalty parameters, as well as a primal feasibility heuristic. I do not think you should have confidence in the algorithm finding an optimal solution, unless the problem is rather simple.
Michael Patriksson , Thanks again ,
well , I do not want to trust it as a reliable optimum.
I seek to understand, if any solution form Relaxed-MINLP , which the GAMS handle the relaxation and returns a solution, can be treated as a lower bound for the original MINLP.
let me know if I'm not clear
No, you can't - first of all you need to have rather precise solution accuracy for each subsolver that you use, to be able to state that something is a lower bound. (That's what would happen if you perform a Lagrangian relaxation, and the subproblem is a mixed-integer program that you do not know will give a correct solution: you cannot always guarantee that the subproblem is solved optimally, and therefore you cannot be sure it is a lower bound.)
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