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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Veröffentlicht in:Operations research letters Jg. 43; H. 4; S. 432 - 437
Hauptverfasser: Yıldız, Sercan, Cornuéjols, Gérard
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.07.2015
Schlagworte:
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-Zugang:Volltext
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Zusammenfassung: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