  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.
