## 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 ...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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