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

Jianlin Jiang (), Liyun Ling (), Yan Gu (), Su Zhang () and Yibing Lv ()
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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

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 1, No 15, 362-389

Abstract: 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.

Keywords: Facility location; Generalized multi-facility Weber problem; Alternating direction method of multipliers; Linearization; Over-relaxation; 90B85; 90C33 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-022-02133-9

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