Distributed Optimization With Coupling Constraints

• 成果类型: Article
• 署名作者: Wu, Xuyang; Wang, He; Lu, Jie
• 署名单位: Royal Institute of Technology; ShanghaiTech University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3169955
• 发表日期: 2023
• 页码: 1847-1854
• 关键词: convergence; Couplings; optimization; Convex functions; linear programming; Distributed algorithms; Transforms; constrained optimization; distributed optimization; primal-dual method; proximal algorithm

摘要

In this article, we investigate distributed convex opti-mization with both inequality and equality constraints, where the objective function can be a general nonsmooth convex function and all the constraints can be both sparsely and densely cou-pling. By strategically integrating ideas from primal-dual, proxi-mal, and virtual-queue optimization methods, we develop a novel distributed algorithm, referred to as IPLUX, to address the prob-lem over a connected, undirected graph. We show that IPLUX achieves an O(1/k) rate of convergence in terms of optimality and feasibility, which is stronger than the convergence results of the alternative methods and eliminates the standard assumption on the compactness of the feasible region. Finally, IPLUX exhibits faster convergence and higher efficiency than several state-of-the-art methods in the simulation.