Minimal Inequalities for an Infinite Relaxation of Integer Programs

The authors show that maximal S-free convex sets are polyhedra when S is the set of integral points in some rational polyhedron of ... This result extends a theorem of Lovasz characterizing maximal lattice-free convex sets. Their theorem has implications in integer programming. In particular, they s...

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Bibliographic Details
Published in:SIAM journal on discrete mathematics 2010-01, Vol.24 (1), p.158-168
Main Authors: Basu, Amitabh, Conforti, Michele, Cornuéjols, Gérard, Zambelli, Giacomo
Format: Article
Language:English
Subjects:
Convex analysis
Inequalities
Integer programming
Integers
Integrals
Lattice theory
Mathematical analysis
Polyhedrons
Studies
Symbols
Theorems
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Summary:The authors show that maximal S-free convex sets are polyhedra when S is the set of integral points in some rational polyhedron of ... This result extends a theorem of Lovasz characterizing maximal lattice-free convex sets. Their theorem has implications in integer programming. In particular, they show that maximal S-free convex sets are in one-to-one correspondence with minimal inequalities. (ProQuest: ... denotes formulae/symbols omitted.)
ISSN:0895-4801
1095-7146
DOI:10.1137/090756375