Cuts for Conic Mixed-Integer Programming

Authors:
Alper Atamtürk;Vishnu Narayanan
Affiliations:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720-1777, USA;Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720-1777, USA
Venue:
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Year:
2007

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Abstract

A conic integer program is an integer programming problem with conic constraints. Conic integer programming has important applications in finance, engineering, statistical learning, and probabilistic integer programming.Here we study mixed-integer sets defined by second-order conic constraints. We describe general-purpose conic mixed-integer rounding cuts based on polyhedral conic substructures of second-order conic sets. These cuts can be readily incorporated in branch-and-bound algorithms that solve continuous conic programming relaxations at the nodes of the search tree. Our preliminary computational experiments with the new cuts show that they are quite effective in reducing the integrality gap of continuous relaxations of conic mixed-integer programs.