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A Complete Characterization of Disjunctive Conic Cuts for Mixed Integer Second Order Cone Optimization

Pietro Belotti(pietrobelotti***at***fico.com)
Julio Goez(Julio.Goez***at***nhh.no)
Imre Polik(imre***at***polik.net)
Ted Ralphs(ted***at***lehigh.edu)
Terlaky Tamas(terlaky***at***lehigh.edu)

Abstract: We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization problem. We extend our prior work on disjunctive conic cuts, which has thus far been restricted to the case in which the intersection of the hyperplanes and the feasible set is bounded. Using a similar technique, we show that one can extend our previous results to the case in which that intersection is unbounded. We provide a complete characterization in closed form of the conic inequalities required to describe the convex hull when the hyperplanes defining the disjunction are parallel.

Keywords: second order cone, mixed integer, convex hull

Category 1: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation: Accepted for publication in Discrete Optimization. Lehigh ISE Tech Report 14T-008 https://ise.lehigh.edu/content/complete-characterization-disjunctive-conic-cuts-mixed-integer-second-order-cone

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Entry Submitted: 10/30/2016
Entry Accepted: 10/30/2016
Entry Last Modified: 10/30/2016

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