Stopping criteria for feasible/infeasible problems with BMIBNB

[David Vázquez Padín]

Dear all,

I'm using the global solver BMIBNB to study the feasibility of a bilinear problem within the YALMIP framework. Everything seems to work fine, but I'm concerned about the criteria used to determine the feasibility of such problem. Assuming that X and Y are two variables of the problem, can I ensure that when a problem is tagged as infeasible (according to the BMIBNB solver), then there is no possible X and Y that can fullfill all the constraints? In other words, can I ensure that the set of possible solutions is empty? (Note: I've adjusted the numer of iterations to Inf and I've also set the maxtime variable to Inf.)

For instance, using only a local solver like fmincon with a starting point to solve the same problem, it seems that the provided solution (in this case, by fmincon) depends on the provided starting point. Therefore, a feasible problem could be tagged as infeasible depending on how good is the supplied starting point. Does it also happen with the global solver BMIBNB, even if no starting point is furnished?

Thank you very much for your help!

Best regards,

David.

[Johan Löfberg]

Proving infeasibility is essentially impossible. The solver branches on variables down to a precision of bmibnb.vartol (default 1e-3), and if the local solver fails to find a solution despite being constrained to such a small regions, YALMIP will report infeasibility.

Is there a particular problem you are working on? You are welcome to send the model for analysis.

[David Vázquez Padín]

Thank you very much for your fast response. I'm starting to work with YALMIP on a possible idea, so I'll be back to you if everything goes well. Thanks again!