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

Santanu S. Dey, Diego A. Morán R.

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)507-526
Number of pages20
JournalMathematical Programming
Volume141
Issue number1-2
DOIs
StatePublished - Oct 2013
Externally publishedYes

Keywords

  • Closedness
  • Convex hull
  • Convex integer program

Fingerprint

Dive into the research topics of 'Some properties of convex hulls of integer points contained in general convex sets'. Together they form a unique fingerprint.

Cite this