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Valid Inequalities and Convex Hulls for Multilinear Functions

hal.structure.identifierDepartment of Industrial and Systems Engineering [Lehigh] [ISE]
dc.contributor.authorBELOTTI, Pietro
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierReformulations based algorithms for Combinatorial Optimization [Realopt]
dc.contributor.authorMILLER, Andrew J.
hal.structure.identifierDepartment of Industrial and Systems Engineering [Wisconsin-Madison] [ISyE]
dc.contributor.authorNAMAZIFAR, Mahdi
dc.date.accessioned2024-04-04T02:27:36Z
dc.date.available2024-04-04T02:27:36Z
dc.date.issued2010
dc.identifier.issn1571-0653
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190032
dc.description.abstractEnWe study the convex hull of the bounded, nonconvex set of a product of n variables for any n ≥ 2. We seek to derive strong valid linear inequalities for this set, which we call M_n; this is motivated by the fact that many exact solvers for nonconvex problems use polyhedral relaxations so as to compute a lower bound via linear programming solvers. We present a class of linear inequalities that, together with the well-known McCormick inequalities, defines the convex hull of M_2. This class of inequalities, which we call lifted tangent inequalities, is uncountably infinite, which is not surprising given that the convex hull of M_n is not a polyhedron. This class of inequalities generalizes directly to M_n for n > 2, allowing us to define strengthened relaxations for these higher dimensional sets as well.
dc.language.isoen
dc.publisherElsevier
dc.title.enValid Inequalities and Convex Hulls for Multilinear Functions
dc.typeArticle de revue
dc.identifier.doi10.1016/j.endm.2010.05.102
dc.subject.halInformatique [cs]/Recherche opérationnelle [cs.RO]
bordeaux.journalElectronic Notes in Discrete Mathematics
bordeaux.page805-812
bordeaux.volume36
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00547924
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00547924v1
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