Convex normalizations in lift-and-project methods for 0-1 programming

Branch-and-Cut algorithms for general 0-1 mixed integer programs can be successfully implemented by using Lift-and-Project (L&P) methods to generate cuts. L&P cuts are drawn from a cone of valid inequalities that is unbounded and, thus, needs to be truncated, or "normalized". We co...

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Bibliographic Details
Published inAnnals of operations research Vol. 116; no. 1; p. 91
Main Authors Rey, Pablo A, Sagastizabal, Claudia A
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.10.2002
Subjects
Algorithms
Computer programming
Convex analysis
Integer programming
Linear programming
Operations research
Studies
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Summary:Branch-and-Cut algorithms for general 0-1 mixed integer programs can be successfully implemented by using Lift-and-Project (L&P) methods to generate cuts. L&P cuts are drawn from a cone of valid inequalities that is unbounded and, thus, needs to be truncated, or "normalized". We consider general normalizations defined by arbitrary closed convex sets and derive dual problems for generating L&P cuts. This unified theoretical framework generalizes and covers a wide group of already known normalizations. We also give conditions for proving finite convergence of the cutting plane procedure that results from using such general L&P cuts. [PUBLICATION ABSTRACT]
ISSN:0254-5330
1572-9338
DOI:10.1023/A:1021320028145