Exponentially Convergent Algorithm Design for Constrained Distributed Optimization via Nonsmooth Approach

• 成果类型: Article
• 署名作者: Li, Weijian; Zeng, Xianlin; Liang, Shu; Hong, Yiguang
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; Beijing Institute of Technology; Tongji University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3075666
• 发表日期: 2022
• 页码: 934-940
• 关键词: convergence; Distributed algorithms; cost function; Heuristic algorithms; resource management; TOPOLOGY; Intelligent control; constrained distributed optimization; exact penalty method; Exponential convergence; nonsmooth approach; projected gradient dynamics

摘要

We develop an exponentially convergent distributed algorithm to minimize a sum of nonsmooth cost functions with a set constraint. The set constraint generally leads to the nonlinearity in distributed algorithms, and results in difficulties to derive an exponential rate. In this article, we remove the consensus constraints by an exact penalty method, and then propose a distributed projected subgradient algorithm by virtue of a differential inclusion and a differentiated projection operator. Resorting to nonsmooth approaches, we prove the convergence for this algorithm, and moreover, provide both the sublinear and exponential rates under some mild assumptions.