A Decentralized Primal-Dual Method for Constrained Minimization of a Strongly Convex Function

• 成果类型: Article
• 署名作者: Hamedani, Erfan Yazdandoost; Aybat, Necdet Serhat
• 署名单位: University of Arizona; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3130082
• 发表日期: 2022
• 页码: 5682-5697
• 关键词: Optimization; Convex functions; communication networks; minimization; Ellipsoids; CONVERGENCE; clocks; convergence analysis; constrained optimization; Distributed algorithms; saddle point problem

摘要

We propose decentralized primal-dual methods for cooperative multiagent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific convex functions over conic constraint sets defined by agent-specific nonlinear functions; hence, the optimal consensus decision should lie in the intersection of these private sets. Under the strong convexity assumption, we provide convergence rates for suboptimality, infeasibility, and consensus violation in terms of the number of communications required; examine the effect of underlying network topology on the convergence rates.