## An Efficient Algorithm for Solving the MAXCUT SDP Relaxation (1998)

Venue: | School of ISyE, Georgie Tech, Atlanta, GA 30332 |

Citations: | 10 - 1 self |

### BibTeX

@TECHREPORT{Burer98anefficient,

author = {Samuel Burer and Renato D.C. Monteiro},

title = {An Efficient Algorithm for Solving the MAXCUT SDP Relaxation},

institution = {School of ISyE, Georgie Tech, Atlanta, GA 30332},

year = {1998}

}

### OpenURL

### Abstract

In this paper we present a projected gradient algorithm for solving the semidefinite programming (SDP) relaxation of the maximum cut (MAXCUT) problem. Coupled with a randomized method, this gives a very efficient approximation algorithm for the MAXCUT problem. We report computational results comparing our method with two earlier successful methods on problems with dimension up to 3000.

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Citation Context ... problems can be naturally relaxed to SDP problems was first observed in Lov'asz [16] and Shor [22] and has been used by several authors (e.g., see [1, 6, 14, 17, 18, 20, 23]). Goemans and Williamson =-=[9]-=- developed a randomized algorithm for the MAXCUT problem, based on solving its SDP relaxation, which provides an approximate solution guaranteed to be within a factor of 0:87856 of its optimal value. ... |

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Citation Context ...n binary (or \Sigma1) variables. The idea that these problems can be naturally relaxed to SDP problems was first observed in Lov'asz [16] and Shor [22] and has been used by several authors (e.g., see =-=[1, 6, 14, 17, 18, 20, 23]-=-). Goemans and Williamson [9] developed a randomized algorithm for the MAXCUT problem, based on solving its SDP relaxation, which provides an approximate solution guaranteed to be within a factor of 0... |

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Citation Context ...problem can be formulated as a quadratic programming (QP) problem in binary (or \Sigma1) variables. The idea that these problems can be naturally relaxed to SDP problems was first observed in Lov'asz =-=[16]-=- and Shor [22] and has been used by several authors (e.g., see [1, 6, 14, 17, 18, 20, 23]). Goemans and Williamson [9] developed a randomized algorithm for the MAXCUT problem, based on solving its SDP... |

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Citation Context ...s for solving the MAXCUT SDP relaxation have recently been developed which take into account its special structure. One approach to solve these problems is with the use of interior-point methods (see =-=[3, 7, 8, 12, 15]-=-). Among The work of these authors was based on research supported by the National Science Foundation under grants INT-9600343 and CCR-9700448. y School of Mathematics, Georgia Tech, Atlanta, Georgia ... |

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Citation Context ...e of the special structure of the MAXCUT SDP relaxation. In addition to interior-point methods, other nonlinear programming methods have recently been proposed to solve the MAXCUT SDP relaxation (see =-=[11, 13]-=-). The approach used in Helmberg and Rendl [11] consists of solving a certain partial Lagrangian dual problem, whose objective function is nondifferentiable, using the usual bundle method for convex p... |

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Citation Context ...s for solving the MAXCUT SDP relaxation have recently been developed which take into account its special structure. One approach to solve these problems is with the use of interior-point methods (see =-=[3, 7, 8, 12, 15]-=-). Among The work of these authors was based on research supported by the National Science Foundation under grants INT-9600343 and CCR-9700448. y School of Mathematics, Georgia Tech, Atlanta, Georgia ... |

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Citation Context ...zed algorithm for solving the semidefinite programming (SDP) relaxation of the maximum cut (MAXCUT) problem. The MAXCUT problem has many applications, e.g. in VLSI design and statistical physics (see =-=[2, 4, 5, 19, 21]-=-). Several algorithms have been proposed to find either exact or approximate solutions to this problem. As for many combinatorial optimization problems, the MAXCUT problem can be formulated as a quadr... |

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Citation Context ...e of the special structure of the MAXCUT SDP relaxation. In addition to interior-point methods, other nonlinear programming methods have recently been proposed to solve the MAXCUT SDP relaxation (see =-=[11, 13]-=-). The approach used in Helmberg and Rendl [11] consists of solving a certain partial Lagrangian dual problem, whose objective function is nondifferentiable, using the usual bundle method for convex p... |

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Citation Context ... formulated as a quadratic programming (QP) problem in binary (or \Sigma1) variables. The idea that these problems can be naturally relaxed to SDP problems was first observed in Lov'asz [16] and Shor =-=[22]-=- and has been used by several authors (e.g., see [1, 6, 14, 17, 18, 20, 23]). Goemans and Williamson [9] developed a randomized algorithm for the MAXCUT problem, based on solving its SDP relaxation, w... |

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