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A Computational Study of Perspective Cuts

  • The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their applicability and computational impact over large, heterogeneous test sets in general-purpose solvers. This paper provides a detailed computational study of perspective cuts within a linear programming based branch-and-cut solver for general mixed-integer nonlinear programs. Within this study, we extend the applicability of perspective cuts from convex to nonconvex nonlinearities. This generalization is achieved by applying a perspective strengthening to valid linear inequalities which separate solutions of linear relaxations. The resulting method can be applied to any constraint where all variables appearing in nonlinear terms are semi-continuous and depend on at least one common indicator variable. Our computational experiments show that adding perspective cuts for convex constraints yields a consistent improvement of performance, and adding perspective cuts for nonconvex constraints reduces branch-and-bound tree sizes and strengthens the root node relaxation, but has no significant impact on the overall mean time.

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Metadaten
Verfasserangaben:Ksenia BestuzhevaORCiD, Ambros GleixnerORCiD, Stefan Vigerske
Dokumentart:Artikel
Titel des übergeordneten Werkes (Englisch):Mathematical Programming Computation
Band:15
Erste Seite:703
Letzte Seite:731
Jahr der Erstveröffentlichung:2023
Preprint:urn:nbn:de:0297-zib-81821
DOI:https://doi.org/10.1007/s12532-023-00246-4
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