Maximal Lattice-Free Convex Sets in Linear Subspaces

被引：61

作者：

Basu, Amitabh ^{[1
]}

Conforti, Michele ^{[2
]}

Cornuejols, Gerard ^{[1
]}

Zambelli, Giacomo ^{[2
]}

机构：

[1] Carnegie Mellon Univ, Tepper Sch Business, Pittsburgh, PA 15213 USA

[2] Univ Padua, Dept Pure & Appl Math, I-35121 Padua, Italy

来源：

MATHEMATICS OF OPERATIONS RESEARCH | 2010年 / 35卷 / 03期

基金：

美国安德鲁·梅隆基金会;

关键词：

geometry of numbers; integer programming; maximal lattice-free convex sets; minimal valid inequalities; SIMPLEX TABLEAU; CUTTING PLANES; INTEGER; INEQUALITIES; VARIABLES; ROWS; CUTS;

D O I：

10.1287/moor.1100.0461

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We consider a model that arises in integer programming and show that all irredundant inequalities are obtained from maximal lattice-free convex sets in an affine subspace. We also show that these sets are polyhedra. The latter result extends a theorem of Lovasz characterizing maximal lattice-free convex sets in R-n.

引用

页码：704 / 720

页数：17

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