An Arrow-Hurwicz-Uzawa type flow as least squares solver for network linear equations

作     者：Liu, Yang Lageman, Christian Anderson, Brian D. O. Shi, Guodong 

作者机构：Australian Natl Univ Res Sch Engn Coll Engn & Comp Sci Canberra ACT 0200 Australia Australian Natl Univ Res Sch Engn Canberra ACT 0200 Australia Univ Wurzburg Inst Math D-97070 Wurzburg Germany Hangzhou Dianzi Univ Hangzhou 310018 Zhejiang Peoples R China 

出 版 物：《AUTOMATICA》 (自动学)

年 卷 期：2019年第100卷

页      面：187-193页

核心收录：

学科分类：0711[理学-系统科学] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071101[理学-系统理论] 

基　　金：DAAD German Federal Ministry of Education and Research (BMBF) Australian Research Council (ARC) [DP-130103610, DP-160104500] 

主　　题：Distributed algorithms Dynamical systems Linear equations Least squares 

摘      要：We study the approach to obtaining least squares solutions to systems of linear algebraic equations over networks by using distributed algorithms. Each node has access to one of the linear equations and holds a dynamic state. The aim for the node states is to reach a consensus as a least squares solution of the linear equations by exchanging their states with neighbors over an underlying interaction graph. A continuous-time distributed least squares solver over networks is developed in the form of the famous Arrow-Hurwicz-Uzawa flow. A necessary and sufficient condition is established on the graph Laplacian for the continuous-time distributed algorithm to give the least squares solution in the limit, with an exponentially fast convergence rate. The feasibility of different fundamental graphs is discussed including path graph and random graph. Moreover, a discrete-time distributed algorithm is developed by Euler s method, converging exponentially to the least squares solution at the node states with suitable step size and graph conditions. (C) 2018 Elsevier Ltd. All rights reserved.