8182 eng reportzib 0 -- 2021-03-15 -- 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. 1438-0064 urn:nbn:de:0297-zib-81821 publish Ksenia Bestuzheva Ksenia Bestuzheva Ambros Gleixner Stefan Vigerske 21-07 eng uncontrolled perspective cuts, mixed-integer nonlinear programming, nonconvex optimization, computational study MATHEMATICAL SOFTWARE Explicit machine computation and programs (not the theory of computation or programming) Computational methods Mixed integer programming Nonconvex programming, global optimization Nonlinear programming Polyhedral combinatorics, branch-and-bound, branch-and-cut Vigerske, Stefan MODAL-SynLab MODAL-Gesamt Mathematical Algorithmic Intelligence AI in Society, Science, and Technology https://opus4.kobv.de/opus4-zib/files/8182/ZR-21-07.pdf