Disjunctive cuts for cross-sections of the second-order cone

In this paper we study general two-term disjunctions on affine cross-sections of the second-order cone. Under some mild assumptions, we derive a closed-form expression for a convex inequality that is valid for such a disjunctive set, and we show that this inequality is sufficient to characterize the...

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Bibliographic Details
Published in:	Operations research letters Vol. 43; no. 4; pp. 432 - 437
Main Authors:	Yıldız, Sercan, Cornuéjols, Gérard
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.07.2015
Subjects:	Cutting planes Disjunctive cuts Mixed-integer conic programming Second-order cone programming Disjunctive cuts Cutting planes Mixed-integer conic programming Second-order cone programming
ISSN:	0167-6377, 1872-7468
Online Access:	Get full text
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Summary:	In this paper we study general two-term disjunctions on affine cross-sections of the second-order cone. Under some mild assumptions, we derive a closed-form expression for a convex inequality that is valid for such a disjunctive set, and we show that this inequality is sufficient to characterize the closed convex hull of all two-term disjunctions on ellipsoids and paraboloids and a wide class of two-term disjunctions–including split disjunctions–on hyperboloids. Our approach relies on the work of Kılınç-Karzan and Yıldız which considers general two-term disjunctions on the second-order cone.
ISSN:	0167-6377 1872-7468
DOI:	10.1016/j.orl.2015.06.001