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Abstract: We present a strengthened semidefinite programming, SDP, relaxation for the Max-Cut, MC, problem. The well known SDP relaxation can be obtained by Lagrangian relaxation and results in a SDP with variable X 2 S n , the space of n \Theta n symmetric matrices, and n constraints. The strengthened bound is based on applying a lifting procedure to this well known semidefinite relaxation while adding nonlinear constraints. The lifting procedure is again done via Lagrangian relaxation. This results... (Update)
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BibTeX entry: (Update)
M. ANJOS and H. WOLKOWICZ. A strengthened sdp relaxation via a second lifting for the max-cut problem. Research report, corr 99-55, University of Waterloo, Waterloo, Ontario, 1999. URL: http://orion.math.uwaterloo.ca/ hwolkowi/henry/reports/strengthMC.ps.gz. http://citeseer.ist.psu.edu/anjos99strengthened.html More
@techreport{ anjos99strengthened,
author = "M. F. Anjos and H. Wolkowicz",
title = "A strengthened {SDP} relaxation via a second lifting for the {MAX-{CUT}} problem",
number = "CORR--95",
address = "Waterloo, Ontario, N2L 3G1 Canada",
year = "1999",
url = "citeseer.ist.psu.edu/anjos99strengthened.html" }
Citations (may not include all citations):415 Improved approximation algorithms for maximum cut and satisf.. - GOEMANS, WILLIAMSON - 1995
173 An interior point method for semidefinite programming - HELMBERG, RENDL et al. - 1996
173 An interior point method for semidefinite programming and ma.. - HELMBERG - 1994
106 approximation algorithms for MAX CUT and MAX 2SAT (context) - GOEMANS, WILLIAMSON - 1994
49 Semidefinite programming in combinatorial optimization - GOEMANS - 1997
46 Laplacian eigenvalues and the maximum cut problem (context) - DELORME, POLJAK - 1993
35 Eigenvalues in combinatorial optimization (context) - MOHAR, POLJAK - 1993
35 Quadratic optimization problems (context) - SHOR - 1987
30 Indefinite trust region subproblems and nonsymmetric eigenva.. - STERN, WOLKOWICZ - 1995
27 Quality of semidefinite relaxation for nonconvex quadratic o.. (context) - NESTEROV - 1997
26 On Lagrangian relaxation of quadratic matrix constraints - ANSTREICHER, WOLKOWICZ - 1998
25 A recipe for semidefinite relaxation (context) - POLJAK, RENDL et al. - 1995
22 Connections between semidefinite relaxations of the max-cut .. - LAURENT, POLJAK et al. - 1997
11 Nonconvex optimization problem: the infinitehorizon linear-q.. (context) - YAKUBOVICH - 1992
5 procedure and duality theorems for nonconvex problems of qua.. (context) - YAKUBOVICH - 1973
4 Strong duality for a trust-region type relaxation of qap - ANSTREICHER, CHEN et al. - 1998
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