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Deletion Presolve for Accelerating Infeasibility Diagnosis in Optimization Models

Whereas much research in the area of optimization is directed toward developing algorithms for optimization of feasible models, the diagnosis of infeasible models has not received as much attention. Identification of irreducible infeasible sets (IISs) can facilitate the process of correcting infeasible models. Several filtering algorithms have been proposed for IIS identification but efficient implementations are available only for linear programs. We propose a novel approach for IIS identification that is applicable to linear programs (LPs), nonlinear programs (NLPs), mixed-integer linear programs (MIPs), and mixed-integer nonlinear programs (MINLPs). The approach makes use of a deletion presolve procedure that exploits bounds tightening techniques to reduce the model to an infeasible set (IS) in a computationally efficient manner. The IS is subsequently reduced to an IIS by applying one of the currently available exact filtering algorithms for IIS identification. We implement the proposed deletion preso...