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Canonical dual approach to solving the maximum cut problem

Author

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  • Zhenbo Wang
  • Shu-Cherng Fang
  • David Gao
  • Wenxun Xing

Abstract

This paper presents a canonical dual approach for finding either an optimal or approximate solution to the maximum cut problem (MAX CUT). We show that, by introducing a linear perturbation term to the objective function, the maximum cut problem is perturbed to have a dual problem which is a concave maximization problem over a convex feasible domain under certain conditions. Consequently, some global optimality conditions are derived for finding an optimal or approximate solution. A gradient decent algorithm is proposed for this purpose and computational examples are provided to illustrate the proposed approach. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Zhenbo Wang & Shu-Cherng Fang & David Gao & Wenxun Xing, 2012. "Canonical dual approach to solving the maximum cut problem," Journal of Global Optimization, Springer, vol. 54(2), pages 341-351, October.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:341-351
    DOI: 10.1007/s10898-012-9881-8
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    References listed on IDEAS

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    1. Francisco Barahona & Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1988. "An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design," Operations Research, INFORMS, vol. 36(3), pages 493-513, June.
    2. David Gao & Ning Ruan, 2010. "Solutions to quadratic minimization problems with box and integer constraints," Journal of Global Optimization, Springer, vol. 47(3), pages 463-484, July.
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    Cited by:

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    2. Yi Chen & David Gao, 2016. "Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions," Journal of Global Optimization, Springer, vol. 64(3), pages 417-431, March.

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