Closedness of integer hulls of simple conic sets

Diego A. Moránr, Santanu S. Dey

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

2 Citas (Scopus)

Resumen

Let C be a full-dimensional pointed closed convex cone in Rm obtained by taking the conic hull of a strictly convex set. Given A ∈ Qm×n1, B ∈ Qm×n2, and b ∈ Qm, a simple conic mixed-integer set (SCMIS) is a set of the form {(x, y) ∈ Zn1 × Rn2 | Ax + By -b ∈ C}. In this paper, we give a complete characterization of the closedness of convex hulls of SCMISs. Under certain technical conditions on the cone C, we show that the closedness characterization can be used to construct a polynomial-time algorithm to check the closedness of convex hulls of SCMISs. Moreover, we also show that the Lorentz cone satisfies these technical conditions. In the special case of pure integer problems, we present sufficient conditions, which can be checked in polynomial time, to verify the closedness of intersection of SCMISs.

Idioma originalInglés
Páginas (desde-hasta)70-99
Número de páginas30
PublicaciónSIAM Journal on Discrete Mathematics
Volumen30
N.º1
DOI
EstadoPublicada - 2016
Publicado de forma externa

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