Disjunctive cuts for Mixed-Integer Conic Optimization

Abstract

Motivated by the recent success of conic formulations for Mixed-Integer Convex Optimization (MICONV), we investigate the impact of disjunctive cutting planes for Mixed-Integer Conic Optimization (MICONIC). We show that conic strong duality, guaranteed by a careful selection of a novel normalization in the conic separation problem, as well as the numerical maturity of interior-point methods for conic optimization allow to solve the theoretical and numerical issues encountered by many authors since the late 90s. As a result, the proposed approach allows algorithmic flexibility in the way the conic separation problem is solved and the resulting cuts are shown to be computationally effective to close a significant amount of gap for a large collection of instances.