Subgradient Based Outer Approximation for Mixed Integer Second Order Cone Programming

Abstract

This paper deals with outer approximation based approaches to solve mixed integer second order cone programs. Thereby the outer approximation is based on subgradients of the second order cone constraints. Using strong duality of the sub-problems that are solved during the algorithm, we are able to determine subgradients satisfying the KKT optimality conditions. This enables us to extend convergence results valid for continuously differentiable mixed integer nonlinear problems to subdifferen-tiable constraint functions. Furthermore, we present a version of the branch-and-bound based outer approximation that converges when relaxing the convergence assumption that every SOCP satisfies the Slater constraint qualification. We give numerical results for some application problems showing the performance of our approach.