Continuous-time Distributed Heavy-ball Algorithm for Distributed Convex Optimization over Undirected and Directed Graphs

作     者：Hao-Ran Yang Wei Ni Hao-Ran Yang;Wei Ni

作者机构：School of ScienceNanchang UniversityNanchang 330031China 

出 版 物：《Machine Intelligence Research》 (机器智能研究（英文版）)

年 卷 期：2022年第19卷第1期

页      面：75-88页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：supported by National Nature Science Foundation of China (Nos. 61663026, 62066026, 61963028 and 61866023) Jiangxi NSF (No. 20192BAB 207025) 

主　　题：Distributed convex optimization second-order distributed algorithm multi-agent systems gradient tracking directed graph 

摘      要：This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization problem by utilizing the gradient tracking strategy, with convergence acceleration being achieved. Both the undirected and unbalanced directed graphs are considered, extending existing algorithms that primarily focus on undirected or balanced directed graphs. Our algorithms also have the advantage of abandoning the diminishing step-size strategy so that slow convergence can be avoided. Furthermore, the exact convergence to the optimal solution can be realized even under the constant step size adopted in this paper. Finally, two numerical examples are presented to show the convergence performance of our algorithms.