Distributed Constrained Optimization Over Unbalanced Directed Networks Using Asynchronous Broadcast-Based Algorithm

• 成果类型: Article
• 署名作者: Li, Huaqing; Lu, Qingguo; Chen, Guo; Huang, Tingwen; Dong, Zhaoyang
• 署名单位: Southwest University - China; University of New South Wales Sydney; Qatar Foundation (QF); Texas A&M University Qatar
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2994024
• 发表日期: 2021
• 页码: 1102-1115
• 关键词: Signal processing algorithms; Convex functions; linear programming; CONVERGENCE; Distributed algorithms; cost function; Asynchronous algorithm; distributed convex optimization; epigraph form; inequality constraints; unbalanced directed networks

摘要

This article focuses on distributed convex optimization problems over an unbalanced directed multiagent (no central coordinator) network with inequality constraints. The goal is to cooperatively minimize the sum of all locally known convex cost functions. Every single agent in the network only knows its local objective function and local inequality constraint, and is constrained to a privately known convex set. Furthermore, we particularly discuss the scenario in which the interactions among agents over the whole network are subjected to possible link failures. To collaboratively solve the optimization problem, we mainly concentrate on an epigraph form of the original constrained optimization to overcome the unbalancedness of directed networks, and propose a new distributed asynchronous broadcast-based optimization algorithm. The algorithm allows that not only the updates of agents are asynchronous in a distributed fashion, but also the step-sizes of all agents are uncoordinated. An important characteristic of the proposed algorithm is to cope with the constrained optimization problem in the case of unbalanced directed networks whose communications are subjected to possible link failures. Under two standard assumptions that the communication network is directly strongly connected and the subgradients of all local objective functions are bounded, we provide an explicit analysis for convergence of the algorithm. Simulation results obtained by three numerical experiments substantiate the feasibility of the algorithm and validate the theoretical findings.