### Distributed Communication-Sliding Mirror-Descent Algorithm for Nonsmooth Resource Allocation Problem

WANG Yinghui1, TU Zhipeng2,3, QIN Huashu2,3

1. 1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
2. Key Lab of Systems and Control, Academy of Mathematics and Systems Science, Beijing 100190, China;
3. University of Chinese Academy of Sciences, Beijing 100190, China
• Received:2020-08-09 Revised:2021-09-14 Online:2022-08-25 Published:2022-08-02
• Supported by:
This research was supported by the National Natural Science Foundation of China under Grant Nos. 72101026, 61621063, and the State Key Laboratory of Intelligent Control and Decision of Complex Systems

WANG Yinghui, TU Zhipeng, QIN Huashu. Distributed Communication-Sliding Mirror-Descent Algorithm for Nonsmooth Resource Allocation Problem[J]. Journal of Systems Science and Complexity, 2022, 35(4): 1244-1261.

This paper considers a distributed nonsmooth resource allocation problem of minimizing a global convex function formed by a sum of local nonsmooth convex functions with coupled constraints. A distributed communication-efficient mirror-descent algorithm, which can reduce communication rounds between agents over the network, is designed for the distributed resource allocation problem. By employing communication-sliding methods, agents can find a ε-solution in O($\frac{1}{\varepsilon }$) communication rounds while maintaining O($\frac{1}{\varepsilon ^2}$) subgradient evaluations for nonsmooth convex functions. A numerical example is also given to illustrate the effectiveness of the proposed algorithm.
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