Distributed Proximal Algorithms for Nonsmooth Optimization: Unified Convergence Analysis

• 成果类型: Article
• 署名作者: Huang, Yi; Cui, Shisheng; Sun, Jian; Meng, Ziyang
• 署名单位: Beijing Institute of Technology; Tsinghua University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3576271
• 发表日期: 2025
• 关键词: convex-optimization; gradient; constraints

摘要

This article studies two classes of nonsmooth distributed optimization problems with coupled constraints, in which the local cost function of each agent consists of a Lipschitz differentiable function and a nonsmooth function. By applying the primal-dual method and proximal operation, we propose two discrete-time distributed algorithms to solve the nonsmooth resource allocation problem and optimal consensus problem, respectively. Different from some previous results with decreasing step-sizes, the proposed algorithms are developed by using the constant step-sizes, which achieves a faster convergence rate. Moreover, we find that these two distributed proximal algorithms have the same structure and can be formulated in a unified framework. A unified convergence analysis is shown that these two algorithms achieve exact convergence to an optimal solution with an ergodic convergence rate O(1/k). Finally, a simulation example is presented to demonstrate the effectiveness of the proposed algorithms.