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A proximal DC approach for quadratic assignment problem

Author

Listed:
  • Zhuoxuan Jiang

    (Beijing University of Technology)

  • Xinyuan Zhao

    (Beijing University of Technology)

  • Chao Ding

    (Chinese Academy of Sciences)

Abstract

In this paper, we show that the quadratic assignment problem (QAP) can be reformulated to an equivalent rank constrained doubly nonnegative (DNN) problem. Under the framework of the difference of convex functions (DC) approach, a semi-proximal DC algorithm is proposed for solving the relaxation of the rank constrained DNN problem whose subproblems can be solved by the semi-proximal augmented Lagrangian method. We show that the generated sequence converges to a stationary point of the corresponding DC problem, which is feasible to the rank constrained DNN problem under some suitable assumptions. Moreover, numerical experiments demonstrate that for most QAP instances, the proposed approach can find the global optimal solutions efficiently, and for others, the proposed algorithm is able to provide good feasible solutions in a reasonable time.

Suggested Citation

  • Zhuoxuan Jiang & Xinyuan Zhao & Chao Ding, 2021. "A proximal DC approach for quadratic assignment problem," Computational Optimization and Applications, Springer, vol. 78(3), pages 825-851, April.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:3:d:10.1007_s10589-020-00252-5
    DOI: 10.1007/s10589-020-00252-5
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    References listed on IDEAS

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    6. Tianxiang Liu & Ting Kei Pong & Akiko Takeda, 2019. "A refined convergence analysis of $$\hbox {pDCA}_{e}$$ pDCA e with applications to simultaneous sparse recovery and outlier detection," Computational Optimization and Applications, Springer, vol. 73(1), pages 69-100, May.
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    Cited by:

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