On a generalization of the Chvatal-Gomory closure

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Many practical integer programming problems involve variables with one or two-sided bounds. Dunkel and Schulz (A refined Gomory-Chvatal closure for polytopes in the unit cube, , 2012) considered a strengthened version of Chvatal-Gomory (CG) inequalities that use 0-1 bounds on variables, and showed that the set of points in a rational polytope that satisfy all these strengthened inequalities is a polytope. Recently, we generalized this result by considering strengthened CG inequalities that use all variable bounds. In this paper, we generalize further by considering not just variable bounds, but general linear constraints on variables. We show that all points in a rational polyhedron that satisfy such strengthened CG inequalities form a rational polyhedron. We also extend this polyhedrality result to mixed-integer sets defined by linear constraints.
Publisher
SPRINGER HEIDELBERG
Issue Date
2022-03
Language
English
Article Type
Article
Citation

MATHEMATICAL PROGRAMMING, v.192, no.1-2, pp.149 - 175

ISSN
0025-5610
DOI
10.1007/s10107-021-01697-0
URI
http://hdl.handle.net/10203/299246
Appears in Collection
IE-Journal Papers(저널논문)
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