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?

  • $\begingroup$ To be interesting, include models for which feasibility is unknown. For instance, for MILP, see twitter.com/Ed_Klotz/status/1186091930582704129 . $\endgroup$ Commented Oct 31, 2019 at 15:38
  • $\begingroup$ 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. $\endgroup$ Commented Oct 31, 2019 at 16:10
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    $\begingroup$ 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. $\endgroup$
    – josliber
    Commented Nov 1, 2019 at 17:43
  • $\begingroup$ @josliber For an MINLP wouldn't that just set the global optimum to another local optimum of the original problem? $\endgroup$ Commented Nov 2, 2019 at 10:38
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    $\begingroup$ @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. $\endgroup$ Commented Nov 2, 2019 at 10:59

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