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Abstract: We study the lift-and-project procedures of Lovász and Schrijver for 0-1 integer programming problems. We prove that the procedure using the positive semidefiniteness constraint is not better than the one without it, in the worst case. Various examples are considered. We also provide geometric conditions characterizing when the positive semidefiniteness constraint does not help. (Update)
Context of citations to this paper: More
...a derivation. A series of lower bounds for various versions of the LS rank were obtained in the context of optimization theory [ST99, CD01, Das01, GT01]. For a counterpart notion in CP, the so called Chv atal rank [Chv73] lower bounds were established in [CCT87, CCH89] To...
...0, and n large, x # j 1 i.e. x # violates (53) by nearly a factor of 2. Related results concerning the N operator are given in [CD01] [GT01], L01] In particular, CD01] shows that starting from the system 1 2 , the N rank of the inequality 1 is n. An open issue concerns...
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BibTeX entry: (Update)
M.X. Goemans and L. Tuncel. When does the positive semidefiniteness constraint help in lifting procedures. Mathematics of Operations Research, to appear. http://citeseer.ist.psu.edu/goemans00when.html More
@techreport{ goemans00when,
author = "M. X. Goemans and L. Tun\ccel",
title = "When does the positive semidefiniteness constraint help in lifting procedures",
address = "Cambridge, MA 02139",
year = "2000",
url = "citeseer.ist.psu.edu/goemans00when.html" }
Citations (may not include all citations):45 The ellipsoid method and its consequences in combinatorial o.. (context) - otschel, Lov et al. - 1981
26 Cones of matrices and set-functions and 0-1 optimization (context) - asz, Schrijver - 1991
18 Disjunctive programming: Properties of the convex hull of fe.. (context) - Balas - 1974
13 Maximum matching and a polyhedron with 0 (context) - Edmonds - 1965
8 a representation of the matching polytope via semidenite lif.. (context) - Optim, Stephen et al. - 1999
6 Convexity in cristallographical lattices (context) - Doignon - 1973
5 private communication (context) - Cook - 1999
2 A lift-and-project cutting plane algorithm for mixed 0-1 pro.. (context) - Research, GSIA et al. - 1993
The graph only includes citing articles where the year of publication is known.
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