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Disjunctive Cuts for Cross-Sections of the Second-Order Cone

Sercan Yildiz(syildiz***at***andrew.cmu.edu)
Gerard Cornuejols(gc0v***at***andrew.cmu.edu)

Abstract: In this paper we provide a unified treatment of general two-term disjunctions on cross-sections of the second-order cone. We derive a closed-form expression for a convex inequality that is valid for such a disjunctive set and show that this inequality is sufficient to characterize the closed convex hull of all two-term disjunctions on ellipsoids and paraboloids, and split disjunctions on all cross-sections of the second-order cone. Our approach extends the work of Kilinc-Karzan and Yildiz on general two-term disjunctions for the second-order cone.

Keywords: Mixed-integer conic programming, second-order cone programming, cutting planes, disjunctive cuts

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )

Citation: Carnegie Mellon University, June 2014

Download: [PDF]

Entry Submitted: 06/10/2014
Entry Accepted: 06/10/2014
Entry Last Modified: 06/10/2014

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