S. Burer, R.D.C. Monteiro, and Y. Zhang. Rank-two relaxation heuristics for MAXCUT and other binary quadratic programs. SIAM J. on Optimization, 12: 503-521, Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Randomized Heuristics for the Max-Cut Problem - Festa, Pardalos, Resende.. (2002) (2 citations) (Correct)
....latter. A variant of the Homer and Peinado algorithm was proposed by Burer and Monteiro [7] Their idea is based on the constrained nonlinear programming reformutation of the MAX CUT semidefinite programming relaxation obtained by a change of variables. More recently, Burer, Monteiro, and Zhang [8] proposed a rank 2 relaxation heuristic for MAX CUT and described a computer code, called circul: that produces better solutions in practice than the randomized algorithm of Goemans and Williamson. The remainder of this paper is organized as follows. In Section 2 we propose various randomized ....
....our heuristics with the randomized algo rithm of Goemans and Williamson [22] to show that the solutions produced by our randomized heuristics are of much better quality than theirs and can be found in a fraction of the time taken by their algorithm. Recently, however, Burer, Monteiro, and Zhang [8] showed that circut, a Fortran 90 implementation of their rank 2 re laxation heuristic for MAX CUT, produces higher quality approximate solutions in practice than the randomized algorithm of Goemans and Williamson. In addition, running times were shown to be small. For this reason, in this ....
[Article contains additional citation context not shown here]
S. Burer, R.D.C. Monteiro, and Y. Zhang. Rank-two relaxation heuristics for MAX-CUT and other binary quadratic programs. SIAM J. on Optimization, 12:503-521, 2001. 2O
A Linear Programming Approach to Semidefinite Programming.. - Krishnan, Mitchell (2001) (1 citation) (Correct)
....primal matrix X as LDiag(d)L T , where L is unit triangular and d # IR n . The constraint that X # 0 is replaced with the requirement that d # 0. The authors show that d is a concave function and give computational results for this reformulation. Finally we must mention that Burer et al. [8, 9] have come up with attractive heuristics for max cut and maximum stable set problems, where they solve (SDP ) with an additional restriction on the rank of the primal matrix X. AN LP APPROACH TO SDP PROBLEMS 3 The spectral bundle method requires the following assumption 1.1, which enables ....
S. Burer, R.D.C. Monteiro and Y. Zhang, Rank-Two Relaxation Heuristics for Max-Cut and Other Binary Quadratic Programs, Working paper, School of ISyE, Georgia Tech., Atlanta, GA, November 2000.
Semi-Infinite Linear Programming Approaches to Semidefinite .. - Krishnan, Mitchell (2001) (Correct)
....problems. We present an overview of this scheme in section 4. Other large scale methods include Burer et al. [10, 11, 12] who formulate (SDP ) as nonconvex programming problems using low rank factorizations of the primal matrix X, and Vanderbei et al. [43] Finally we must mention that Burer et al. [13, 14] have come up with attractive heuristics for max cut and maximum stable set problems, where they solve (SDP ) with an additional restriction on the rank of the primal matrix X. The primary objective in this paper is to develop an LP approach to solving (SDP ) The aim is to utilize some of the ....
S. Burer, R.D.C. Monteiro and Y. Zhang, Rank-Two Relaxation Heuristics for Max-Cut and Other Binary Quadratic Programs, Working paper, School of ISyE, Georgia Tech., Atlanta, GA, November 2000.
Scientific Computing Research Environments for the.. - Heinkenschloss.. (2001) Self-citation (Zhang) (Correct)
No context found.
S. Burer, R. Monteiro, and Y. Zhang. Rank-two relaxation heuristics for max-cut and other binary quadratic programs. SIAM journal on Optimization, To appear, 2001.
Maximum Stable Set Formulations and Heuristics Based on.. - Burer, Monteiro, Zhang (2000) (5 citations) Self-citation (Burer Monteiro Zhang) (Correct)
.... can (1) be exploited to find large stable sets in G To the best of our knowledge, no methods to provide such lower bounds have been proposed (though Benson and Ye [1] have solved an alternative SDP formulation for the Lovasz theta number #(G) to generate stable sets in G) In a recent paper [5], the authors of the present paper have considered another combinatorial optimization problem the Max Cut problem on G in a similar context as we now consider the MSS problem. The SDP relaxation of Max Cut is well known to provide both a good upper bound on the maximum cut size as well as ....
....in a similar context as we now consider the MSS problem. The SDP relaxation of Max Cut is well known to provide both a good upper bound on the maximum cut size as well as the ability to obtain guaranteed highquality cuts in G via the Goemans Williamson randomization scheme (see [7] The focus of [5] was to develop fast methods for finding high quality cuts in G, and so instead of solving the expensive SDP relaxation for Max Cut, the authors restricted the rank of the matrix variable of the relaxation to be at most two and applied a modified Goemans Williamson scheme to the rank two ....
[Article contains additional citation context not shown here]
S. Burer, R. D. C. Monteiro and Y. Zhang. Rank-two relaxation heuristics for max-cut and other binary quadratic programs. Manuscript, School of Industrial and Systems Engineering, Atlanta, GA, USA, November 2000.
Maximum Stable Set Formulations and Heuristics Based on.. - Burer, Monteiro, Zhang (2000) (5 citations) Self-citation (Burer Monteiro Zhang) (Correct)
.... can (1) be exploited to find large stable sets in G To the best of our knowledge, no methods to provide such lower bounds have been proposed (though Benson and Ye [1] have solved an alternative SDP formulation for the Lov asz theta number #(G) to generate stable sets in G) In a recent paper [5], the authors of the present paper have considered another combinatorial optimization problem the Max Cut problem on G in a similar context as we now consider the MSS problem. The SDP relaxation of Max Cut is well known to provide both a good upper bound on the maximum cut size as well as ....
....in a similar context as we now consider the MSS problem. The SDP relaxation of Max Cut is well known to provide both a good upper bound on the maximum cut size as well as the ability to obtain guaranteed highquality cuts in G via the Goemans Williamson randomization scheme (see [7] The focus of [5] was to develop fast methods for finding high quality cuts in G, and so instead of solving the expensive SDP relaxation for Max Cut, the authors restricted the rank of the matrix variable of the relaxation to be at most two and applied a modified Goemans Williamson scheme to the rank two ....
[Article contains additional citation context not shown here]
S. Burer, R. D. C. Monteiro and Y. Zhang. Rank-two relaxation heuristics for max-cut and other binary quadratic programs. Manuscript, School of Industrial and Systems Engineering, Atlanta, GA, USA, November 2000.
Int. J. of Computational Science and Engineering, Vol. 1.. - Max-Cut Problem Sera (Correct)
No context found.
S. Burer, R.D.C. Monteiro, and Y. Zhang. Rank-two relaxation heuristics for MAXCUT and other binary quadratic programs. SIAM J. on Optimization, 12: 503-521,
Constructing Test Functions for Global Optimization Using.. - Balasundaram, Butenko (2005) (Correct)
No context found.
Burer, S., Monteiro, R. D. C. and Zhang, Y., 2001, Rank-two relaxation heuristics for MAX-CUT and other binary quadratic programs. SIAM Journal on Optimization, 12, 503-521.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC