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.
| Author: | Ksenia BestuzhevaORCiD, Ambros GleixnerORCiD, Stefan Vigerske |
|---|---|
| Document Type: | Article |
| Parent Title (English): | Mathematical Programming Computation |
| Volume: | 15 |
| First Page: | 703 |
| Last Page: | 731 |
| Year of first publication: | 2023 |
| Preprint: | urn:nbn:de:0297-zib-81821 |
| DOI: | https://doi.org/10.1007/s12532-023-00246-4 |

