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A comparison of the Sherali-Adams, Lovász-Schrijver and Lasserre relaxations for 0-1 programming (2001) [35 citations — 5 self]

Abstract:

Citations

803 Geometric algorithms and combinatorial optimization. Second edition – Grötschel, Lovasz, et al. - 1993
615 Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming – Goemans, Williamson - 1995
227 On the Shannon capacity of a graph – Lovász - 1979
167 Cones of matrices and set-functions and 0−1 optimization – Lovász, Schrijver - 1991
165 Geometry of Cuts and Metrics – Deza, Laurent - 1997
154 A Lift-and-Project Cutting Plane Algorithm for Mixed 0-1 – Balas, Ceria, et al. - 1993
120 Global optimization with polynomials and the problem of moments – Lasserre
101 A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems – Sherali, Adams - 1990
98 Edmonds polytopes and a hierarchy of combinatorial problems. Discrete Mathematics – Chvatal - 1973
79 On the cut polytope – Barahona, Mahjoub - 1986
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59 The k-moment problem for compact semialgebraic sets – Schmudgen - 1991
56 Squared Functional Systems and Optimization Problems. Chapter 17 – Nesterov - 2000
55 Harmonic Analysis on Semigroups (Theory of Positive Definite – Berg, Christensen, et al. - 1984
29 Semidefinite programming relaxation for nonconvex quadratic programs – Fujie, Kojima - 1997
28 An explicit exact SDP relaxation for nonlinear 0−1 programs – Lasserre - 2001
26 On cutting-plane proofs in combinatorial optimization. Linear Algebra and its Applications – Chvatal, Cook, et al. - 1989
23 Bounds on the Chvatal rank of polytopes in the 0/1cube – Eisenbrand, Schulz - 1999
23 Approximating the stability number of a graph via copositive programming – Klerk, Pasechnik
22 On the matrix-cut rank of polyhedra – Cook, Dash - 2001
21 When does the positive semidefiniteness constraint help in lifting procedures – Goemans, Tuncel - 2000
21 Nondifferentiable Optimization and Polynomial Problems – Shor - 1998
19 On the membership problem for the elementary closure of a polyhedron – Eisenbrand - 1999
18 Strengthened semidefinite relaxations via a second lifting for the max-cut problem – Anjos, Wolkowicz - 2002
18 The truncated complex K-moment problem – Curto, Fialkow
17 On a representation of the matching polytope via semidefinite liftings – Stephen, Tuncel - 1999
13 The multidimensional moment problem – FUGLEDE - 1983
12 Hadamard determinants, möbius functions, and the chromatic number of a graph – Wilf - 1968
10 On the rank of mixed 0-1 polyhedra – Cornuejols, Li
9 Optimality conditions and LMI relaxations for 0-1 programs – Lasserre - 2000
8 A remark on the multidimensional moment problem, Mathematische Annalen 243:163–169 – Berg, Christensen, et al. - 1979
7 Tighter linear and semidefinite relaxations for max-cut based on the LovaszSchrijver lift-and-project procedure – Laurent
7 Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization – Parillo - 2000
6 On the momentum problem for distributions in more than one dimension – Haviland - 1935
5 An approach to obtaining global extremums in polynomial mathematical programming problems – Shor - 1987
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