Distributed Mirror Descent Algorithm With Bregman Damping for Nonsmooth Constrained Optimization

• 成果类型: Article
• 署名作者: Chen, Guanpu; Xu, Gehui; Li, Weijian; Hong, Yiguang
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Alibaba Group; Tongji University; Tongji University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3244995
• 发表日期: 2023
• 页码: 6921-6928
• 关键词: Constrained optimization; Distributed algorithm; mirror descent; Multi-agent system; nonsmooth.

摘要

To efficiently solve the nonsmooth distributed optimization with both local constraints and coupled constraints, we propose a distributed continuous-time algorithm based on the mirror descent (MD) method. In this article, we introduce the Bregman damping into distributed MD-based dynamics, which not only successfully applies the MD idea to the distributed primal-dual framework, but also ensures the boundedness of all variables and the convergence of the entire dynamics. Our approach generalizes the classic distributed projection-based dynamics, and establishes a connection between MD methods and distributed Euclidean-projected approaches. Also, we prove the convergence of the proposed distributed dynamics with an O(1/t) rate. For practical implementation, we further give a discrete-time algorithm based on the proposed dynamics with an O(1/root k) convergence rate.