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Canonical dual approach to solving the maximum cut problem


  • Zhenbo Wang


  • Shu-Cherng Fang


  • David Gao


  • Wenxun Xing



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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    Cited by:

    1. Vittorio Latorre & Simone Sagratella, 2016. "A canonical duality approach for the solution of affine quasi-variational inequalities," Journal of Global Optimization, Springer, vol. 64(3), pages 433-449, March.
    2. Yi Chen & David Y. 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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