A Computational Comparison of Reformulations of the Perspective Relaxation: SOCP vs. Cutting Planes

The Perspective Reformulation is a general approach for constructing tight approximations to MINLP problems with semicontinuous variables. Two different reformulations have been proposed for solving it, one resulting in a Second-Order Cone Program, the other based on representing the perspective function by (an infinite number of) cutting planes. We compare the two reformulations on two sets of MIQPs to determine which one is most effective in the context of exact or approximate Branch-and-Cut algorithms.