DISA: A Dual Inexact Splitting Algorithm for Distributed Convex Composite Optimization

• 成果类型: Article
• 署名作者: Guo, Luyao; Shi, Xinli; Yang, Shaofu; Cao, Jinde
• 署名单位: Southeast University - China; Southeast University - China; Southeast University - China; Southeast University - China; Southeast University - China; Purple Mountain Laboratories; Southeast University - China; Yonsei University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3301289
• 发表日期: 2024
• 页码: 2995-3010
• 关键词: Distributed composite optimization; larger step size; primal-dual proximal splitting

摘要

In this article, we propose a novel dual inexact splitting algorithm (DISA) for distributed convex composite optimization problems, where the local loss function consists of a smooth term and a possibly nonsmooth term composed of a linear mapping. The DISA, for the first time, eliminates the dependence of the convergent step-size range on the Euclidean norm of the linear mapping, while inheriting the advantages of the classic primal-dual proximal splitting algorithm (PD-PSA): simple structure and easy implementation. This indicates that the DISA can be executed without prior knowledge of the norm, and tiny step sizes can be avoided when the norm is large. In addition, we prove sublinear and linear convergence rates of DISA under general convexity and metric subregularity, respectively. Moreover, we provide a variant of DISA with approximate proximal mapping and prove its global convergence and sublinear convergence rate. Numerical experiments corroborate our theoretical analyses and demonstrate a significant acceleration of the DISA compared to the existing PD-PSAs