ADMM-type methods for generalized multi-facility Weber problem
ADMM-type methods for generalized multi-facility Weber problem
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DOI：
10.3934/jimo.2020171
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发表时间：
2020
影响因子：
1.3
通讯作者：
Shun Zhang;Jianlin Jiang;Su Zhang;Yibing Lv;Yuzhen Guo
中科院分区：
文献类型：
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作者：
Shun Zhang;Jianlin Jiang;Su Zhang;Yibing Lv;Yuzhen Guo
著名的多设施韦伯问题（MFWP）是设施选址的基本模型之一。为了提高MFWP的实用性，考虑了一个广义多设施韦伯问题（GMFWP），该问题中，使用量规测量距离，并对新设施施加位置约束.本文主要研究基于交替方向乘子法（ADMM）的求解GMFWP的高效数值方法。具体地说，GMFWP被等价地转化为一个具有特殊结构的极小极大问题，然后对它的原问题提出了一些ADMM型方法。在较弱的假设下证明了GMFWP方法的全局收敛性。初步的数值结果报告，以验证所提出的方法的有效性。
The well-known multi-facility Weber problem (MFWP) is one of fundamental models in facility location. With the aim of enhancing the practical applicability of MFWP, this paper considers a generalized multi-facility Weber problem (GMFWP), where the gauge is used to measure distances and the locational constraints are imposed to new facilities. This paper focuses on developing efficient numerical methods based on alternating direction method of multipliers (ADMM) to solve GMFWP. Specifically, GMFWP is equivalently reformulated into a minmax problem with special structure and then some ADMM-type methods are proposed for its primal problem. Global convergence of proposed methods for GMFWP is established under mild assumptions. Preliminary numerical results are reported to verify the effectiveness of proposed methods.