Local cuts for mixed-integer programming

A general framework for cutting-plane generation was proposed by Applegate et al. in the context of the traveling salesman problem. The process considers the image of a problem space under a linear mapping, chosen so that a relaxation of the mapped problem can be solved efficiently. Optimization in...

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Bibliographic Details
Published inMathematical programming computation Vol. 5; no. 2; pp. 171 - 200
Main Authors Chvátal, Vašek, Cook, William, Espinoza, Daniel
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.06.2013
Subjects
Full Length Paper
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Optimization
Theory of Computation
90C57
90C11
65K05
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ISSN1867-2949
1867-2957
DOI10.1007/s12532-013-0052-9

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Summary:A general framework for cutting-plane generation was proposed by Applegate et al. in the context of the traveling salesman problem. The process considers the image of a problem space under a linear mapping, chosen so that a relaxation of the mapped problem can be solved efficiently. Optimization in the mapped space can be used to find a separating hyperplane, if one exists, and via substitution this gives a cutting plane in the original space. We extend this procedure to general mixed-integer programming problems, obtaining a range of possibilities for new sources of cutting planes. Some of these possibilities are explored computationally, both in floating-point arithmetic and in rational arithmetic.
ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-013-0052-9