# Is there a library of infeasible MINLP problems?

We have a number of test libraries to test solver performance like MINLPLIB, QPLIB, etc., but the problems in all libraries I know are overwhelmingly on the feasible side.

Is there a library to test a solver's ability to prove infeasibility?

• To be interesting, include models for which feasibility is unknown. For instance, for MILP, see twitter.com/Ed_Klotz/status/1186091930582704129 . – Mark L. Stone Oct 31 '19 at 15:38
• here is a long list of NLP and MINLP test problems (minlp.com/nlp-and-minlp-test-problems) you may find some test problems for infeasible ones as well. – Oguz Toragay Oct 31 '19 at 16:10
• For any feasible library instance with objective function $f(x)$ that we are maximizing and a known optimal objective value $o$, you could add a constraint $f(x) \ge o+1$ to get an infeasible problem instance. So my guess is that you could pretty easily build such a library from existing ones. – josliber Nov 1 '19 at 17:43
• @josliber For an MINLP wouldn't that just set the global optimum to another local optimum of the original problem? – Nikos Kazazakis Nov 2 '19 at 10:38
• @nikaza Presumably josliber intends $\alpha$ to be the global maximum objective value, so adding the stated constraint renders the problem infeasible. Perhaps you read it as minimum, not maximum. .... While these would be infeasible problems, hopefully they would only be a part of an infeasible problem library, because all the infeasibilities would be of the same type, due to a single inequality involving the objective function. – Mark L. Stone Nov 2 '19 at 10:59