research-article

A Semidefinite Programming Based Polyhedral Cut and Price Approach for the Maxcut Problem

Authors:

Kartik Krishnan,

John E. MitchellAuthors Info & Claims

Computational Optimization and Applications, Volume 33, Issue 1

Pages 51 - 71

https://doi.org/10.1007/s10589-005-5958-3

Published: 01 January 2006 Publication History

Abstract

We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the well-known SDP relaxation of maxcut is formulated as a semi-infinite linear programming problem, which is solved within an interior point cutting plane algorithm in a dual setting; this constitutes the pricing (column generation) phase of the algorithm. Cutting planes based on the polyhedral theory of the maxcut problem are then added to the primal problem in order to improve the SDP relaxation; this is the cutting phase of the algorithm. We provide computational results, and compare these results with a standard SDP cutting plane scheme.

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Cited By

Wang YTanaka AYoshise A(2021)Polyhedral approximations of the semidefinite cone and their applicationComputational Optimization and Applications10.1007/s10589-020-00255-278:3(893-913)Online publication date: 2-Jan-2021
https://dl.acm.org/doi/10.1007/s10589-020-00255-2
Gu SYang Y(2018)A Pointer Network Based Deep Learning Algorithm for the Max-Cut ProblemNeural Information Processing10.1007/978-3-030-04167-0_22(238-248)Online publication date: 13-Dec-2018
https://dl.acm.org/doi/10.1007/978-3-030-04167-0_22
Ahmadi ADash SHall G(2017)Optimization over structured subsets of positive semidefinite matrices via column generationDiscrete Optimization10.1016/j.disopt.2016.04.00424:C(129-151)Online publication date: 1-May-2017
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Index Terms

A Semidefinite Programming Based Polyhedral Cut and Price Approach for the Maxcut Problem
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
      1. Continuous optimization
        Linear programming
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
      1. Continuous optimization
        Linear programming

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Computational Optimization and Applications

Computational Optimization and Applications Volume 33, Issue 1

Jan 2006

103 pages

ISSN:0926-6003

Issue’s Table of Contents

© Springer Science + Business Media, Inc. 2006.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 January 2006

Accepted: 12 September 2005

Revision received: 08 September 2005

Received: 25 May 2004

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Cited By

Wang YTanaka AYoshise A(2021)Polyhedral approximations of the semidefinite cone and their applicationComputational Optimization and Applications10.1007/s10589-020-00255-278:3(893-913)Online publication date: 2-Jan-2021
https://dl.acm.org/doi/10.1007/s10589-020-00255-2
Gu SYang Y(2018)A Pointer Network Based Deep Learning Algorithm for the Max-Cut ProblemNeural Information Processing10.1007/978-3-030-04167-0_22(238-248)Online publication date: 13-Dec-2018
https://dl.acm.org/doi/10.1007/978-3-030-04167-0_22
Ahmadi ADash SHall G(2017)Optimization over structured subsets of positive semidefinite matrices via column generationDiscrete Optimization10.1016/j.disopt.2016.04.00424:C(129-151)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1016/j.disopt.2016.04.004
Zhou XGao DYang CGui W(2016)Discrete state transition algorithm for unconstrained integer optimization problemsNeurocomputing10.1016/j.neucom.2015.08.041173:P3(864-874)Online publication date: 15-Jan-2016
https://dl.acm.org/doi/10.1016/j.neucom.2015.08.041
Sun SPeng QZhang X(2016)Global feature selection from microarray data using Lagrange multipliersKnowledge-Based Systems10.1016/j.knosys.2016.07.035110:C(267-274)Online publication date: 15-Oct-2016
https://dl.acm.org/doi/10.1016/j.knosys.2016.07.035
Wu QWang YLü Z(2015)A tabu search based hybrid evolutionary algorithm for the max-cut problemApplied Soft Computing10.1016/j.asoc.2015.04.03334:C(827-837)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1016/j.asoc.2015.04.033
Shylo VGlover FSergienko I(2015)Teams of Global Equilibrium Search Algorithms for Solving the Weighted Maximum Cut Problem in ParallelCybernetics and Systems Analysis10.1007/s10559-015-9692-251:1(16-24)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1007/s10559-015-9692-2
Benlic UHao J(2013)Breakout Local Search for the Max-CutproblemEngineering Applications of Artificial Intelligence10.1016/j.engappai.2012.09.00126:3(1162-1173)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1016/j.engappai.2012.09.001
Wu QHao J(2013)Memetic search for the max-bisection problemComputers and Operations Research10.1016/j.cor.2012.06.00140:1(166-179)Online publication date: 1-Jan-2013
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Kochenberger GHao JLü ZWang HGlover F(2013)Solving large scale Max Cut problems via tabu searchJournal of Heuristics10.1007/s10732-011-9189-819:4(565-571)Online publication date: 1-Aug-2013
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