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

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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.

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Authors and Affiliations

  1. School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Jianlin Jiang, Liyun Ling & Yan Gu

  2. Business School, Nankai University, Tianjin, 300071, China

    Su Zhang

  3. School of Information and Mathematics, Yangtze University, Jingzhou, 434023, China

    Yibing Lv

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  1. Jianlin Jiang
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  2. Liyun Ling
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  3. Yan Gu
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  4. Su Zhang
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  5. Yibing Lv
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Correspondence to Su Zhang.

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Communicated by Christiane Tammer.

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The first author was supported by National Natural Science Foundation of China No. 11971230. The third author was supported by National Natural Science Foundation of China No. 12201295 and Natural Science Foundation of Jiangsu Province of China No. BK20210267. The fourth author was supported by National Natural Science Foundation of China No. 12071234.

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Jiang, J., Ling, L., Gu, Y. et al. Customized Alternating Direction Methods of Multipliers for Generalized Multi-facility Weber Problem. J Optim Theory Appl 196, 362–389 (2023). https://doi.org/10.1007/s10957-022-02133-9

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  • DOI: https://doi.org/10.1007/s10957-022-02133-9

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