Computation of the Lasserre Ranks of Some Polytopes

Over the years, various lift-and-project methods have been proposed to construct hierarchies of successive linear or semidefinite relaxations of a 0–1 polytope P n that converge to P in n steps. Many such methods have been shown to require n steps in the worst case. In this paper, we show that the m...

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Bibliographic Details
Published inMathematics of operations research Vol. 32; no. 1; pp. 88 - 94
Main Author Cheung, Kevin K. H
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.02.2007
Institute for Operations Research and the Management Sciences
Subjects
0-1 polytope
Combinatorial optimization
Computer software
Hierarchies
Integer programming
Integers
Lasserre rank
lift and project
Mathematical theorems
Mathematical vectors
Operations research
Polyhedrons
Polynomials
Polytopes
semidefinite relaxation
Studies
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Summary:Over the years, various lift-and-project methods have been proposed to construct hierarchies of successive linear or semidefinite relaxations of a 0–1 polytope P n that converge to P in n steps. Many such methods have been shown to require n steps in the worst case. In this paper, we show that the method of Lasserre also requires n steps in the worst case.
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.1060.0212