Some properties of convex hulls of integer points contained in general convex sets

Santanu S. Dey, Diego A. Morán R.

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

18 Citas (Scopus)

Resumen

In this paper, we study properties of general closed convex sets that determine the closedness and polyhedrality of the convex hull of integer points contained in it. We first present necessary and sufficient conditions for the convex hull of integer points contained in a general convex set to be closed. This leads to useful results for special classes of convex sets such as pointed cones, strictly convex sets, and sets containing integer points in their interior. We then present a sufficient condition for the convex hull of integer points in general convex sets to be a polyhedron. This result generalizes the well-known result due to Meyer (Math Program 7:223-225, 1974). Under a simple technical assumption, we show that these sufficient conditions are also necessary for the convex hull of integer points contained in general convex sets to be a polyhedron.

Idioma originalInglés
Páginas (desde-hasta)507-526
Número de páginas20
PublicaciónMathematical Programming
Volumen141
N.º1-2
DOI
EstadoPublicada - oct. 2013
Publicado de forma externa

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