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An efficient Lagrangian smoothing heuristic for Max-Cut

Author

Listed:
  • Yong Xia

    (Beihang University)

  • Zi Xu

    (Beihang University)

Abstract

Max-Cut is a famous NP-hard problem in combinatorial optimization. In this article, we propose a Lagrangian smoothing algorithm for Max-Cut, where the continuation subproblems are solved by the truncated Frank-Wolfe algorithm. We establish practical stopping criteria and prove that our algorithm finitely terminates at a KKT point, the distance between which and the neighbour optimal solution is also estimated. Additionally, we obtain a new sufficient optimality condition for Max-Cut. Numerical results indicate that our approach outperforms the existing smoothing algorithm in less time.

Suggested Citation

  • Yong Xia & Zi Xu, 2010. "An efficient Lagrangian smoothing heuristic for Max-Cut," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(5), pages 683-700, October.
    • Handle: RePEc:spr:indpam:v:41:y:2010:i:5:d:10.1007_s13226-010-0039-4
    DOI: 10.1007/s13226-010-0039-4
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    References listed on IDEAS

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    1. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
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