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Customized Alternating Direction Methods of Multipliers for Generalized Multi-facility Weber Problem

Author

Listed:
  • Jianlin Jiang

    (Nanjing University of Aeronautics and Astronautics)

  • Liyun Ling

    (Nanjing University of Aeronautics and Astronautics)

  • Yan Gu

    (Nanjing University of Aeronautics and Astronautics)

  • Su Zhang

    (Nankai University)

  • Yibing Lv

    (Yangtze University)

Abstract

This paper addresses a generalized multi-facility Weber problem (GMFWP) where the gauge is used to measure distance and locational constraints are imposed on new facilities. This problem has important applications in real situations, either itself or as subproblems. In order to solve GMFWP efficiently, we reformulate it as a separable minimization problem and then two customized alternating direction methods of multipliers (ADMMs) based on augmented Lagrangian function are contributed to solving the resulted separable problem. Specifically, for unconstrained GMFWP, a convergent ADMM for two-block problem is presented. For constrained GMFWP, the direct application of ADMM for multi-block problem has no convergence guarantee. As one of main contributions, this paper proposes a new ADMM for the general multi-block separable problem, and its global convergence is established under mild assumptions. We then apply the new convergent ADMM to solve constrained GMFWP. Some satisfactory numerical results for numerous GMFWPs are reported, which verify the efficiency of proposed ADMM algorithms.

Suggested Citation

  • Jianlin Jiang & Liyun Ling & Yan Gu & Su Zhang & Yibing Lv, 2023. "Customized Alternating Direction Methods of Multipliers for Generalized Multi-facility Weber Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 362-389, January.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:1:d:10.1007_s10957-022-02133-9
    DOI: 10.1007/s10957-022-02133-9
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    References listed on IDEAS

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    1. B. S. He & H. Yang & S. L. Wang, 2000. "Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 337-356, August.
    2. J. B. Rosen & G. L. Xue, 1993. "On the Convergence of a Hyperboloid Approximation Procedure for the Perturbed Euclidean Multifacility Location Problem," Operations Research, INFORMS, vol. 41(6), pages 1164-1171, December.
    3. William Miehle, 1958. "Link-Length Minimization in Networks," Operations Research, INFORMS, vol. 6(2), pages 232-243, April.
    4. Jianlin Jiang & Su Zhang & Yibing Lv & Xin Du & Ziwei Yan, 2020. "An ADMM-based location–allocation algorithm for nonconvex constrained multi-source Weber problem under gauge," Journal of Global Optimization, Springer, vol. 76(4), pages 793-818, April.
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