The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0–1 Programming
Open accessAbstract
Sherali and Adams (1990), Lovász and Schrijver (1991) and, recently, Lasserre (2001b) have constructed hierarchies of successive linear or semidefinite relaxations of a 0–1 polytope P ⫅ ℝ n converging to P in n steps. Lasserre's approach uses results about representations of positive polynomials as sums of squares and the dual theory of moments. We present the three methods in a common elementary framework and show that the Lasserre construction provides the tightest relaxations of P. As an application this gives a direct simple proof for the convergence of the Lasserre's hierarchy. We describe applications to the stable set polytope and to the cut polytope.
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Cites
Goemans, M. X., & Williamson, D. P. (1995) · Journal of the ACM · doi:10.1145/227683.227684 · Cited by 3,587
Geometric Algorithms and Combinatorial Optimization
Grötschel, M., Lovász, L., & Schrijver, A. (1988) · Algorithms and Combinatorics · doi:10.1007/978-3-642-97881-4 · Cited by 3,431
Global Optimization with Polynomials and the Problem of Moments
Lasserre, J. B. (2001) · SIAM Journal on Optimization · doi:10.1137/s1052623400366802 · Cited by 2,474
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
Parrilo, P. A. (2000) · doi:10.7907/2k6y-ch43 · Cited by 1,802
On the Shannon capacity of a graph
Lovasz, L. (1979) · IEEE Transactions on Information Theory · doi:10.1109/tit.1979.1055985 · Cited by 1,624
Harmonic Analysis on Semigroups
Berg, C., Christensen, J. P. R., & Ressel, P. (1984) · Graduate Texts in Mathematics · doi:10.1007/978-1-4612-1128-0 · Cited by 1,134
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Self-citationCones of Matrices and Set-Functions and 0–1 Optimization
Lovász, L., & Schrijver, A. (1991) · SIAM Journal on Optimization · doi:10.1137/0801013 · Cited by 1,008
Sherali, H. D., & Adams, W. P. (1990) · SIAM Journal on Discrete Mathematics · doi:10.1137/0403036 · Cited by 931
Edmonds polytopes and a hierarchy of combinatorial problems
Chvátal, V. (1973) · Discrete Mathematics · doi:10.1016/0012-365x(73)90167-2 · Cited by 624
Cited by
Learning dynamic polynomial proofs
Fawzi, A., Malinowski, M., Fawzi, H., & Fawzi, O. (2019) · arXiv · doi:10.48550/arxiv.1906.01681 · Cited by 8
Metadata
- Authors
- Laurent, M.
- Venue
- Mathematics of Operations Research
- Published
- 2003-08
- Volume
- 28
- Issue
- 3
- Pages
- 470-496
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2077397558
- Cited by
- 373
- References
- 22
- FWCI
- 14.25
- Type
- journal article
- Language
- en
- Open access
- green
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- Laurent, M. (2003). A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0–1 Programming. Mathematics of Operations Research. https://doi.org/10.1287/moor.28.3.470.16391
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