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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?

LarrySnyder610
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Nikos Kazazakis
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  • To be interesting, include models for which feasibility is unknown. For instance, for MILP, see https://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 (https://www.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
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    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 01 '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 02 '19 at 10:38
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    @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 02 '19 at 10:59
  • @MarkL.Stone Ah yes, I missed the maximization part, you are right :) – Nikos Kazazakis Nov 02 '19 at 11:01

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You can check the following weblink:

https://www.minlp.com/nlp-and-minlp-test-problems

1137h4xor
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  • Do you know which and how many of these within each library are infeasible? Anyhow, you should also add this to https://or.stackexchange.com/questions/244/optimization-problem-libraries . – Mark L. Stone Mar 18 '23 at 11:27