有向网络上随机—闲聊设置下的一个动量加速算法  

A Momentum Acceleration Algorithm over Directed Networks Under Random-gossip Setting

作　　者：袁纪彪 任冬梅 YUAN Jibiao;REN Dongmei(College of Science,Hebei University of Technology,Tianjin,300401,P.R.China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《数学进展》2024年第2期407-424,共18页Advances in Mathematics（China）

摘　　要：本文考虑一个分布式优化问题,其中整个网络上智能体之间的交互可能会发生链路故障,并在随机—闲聊设置下提出了一个有向网络上的动量加速算法.在目标函数是强凸且光滑的假设下,从理论上证明了所提出的算法可以线性收敛到精确解.由于使用了重球动量项,所提出的算法可以更快地收敛到精确解.数值结果表明,与现有的分布式算法相比,该算法能够更快地收敛到精确解,特别是对于病态问题.In this paper,we consider a distributed optimization problem where the interactions among agents over the whole network are subjected to possible link failures,and propose a momentum acceleration algorithm over directed networks under random-gossip setting.Under the assumption that the objective function is strongly convex and smooth,it is theoretically proved that the proposed algorithm can converge linearly to an exact solution.Due to the use of the heavy-ball momentum term,the proposed algorithm can converge to an exact solution faster.Numerical results show that the proposed algorithm can converge to an exact solution faster than some existing distributed algorithms,especially for ill-conditioned problems.

关 键 词：分布式优化 有向网络 随机—闲聊算法 线性收敛 

分 类 号：O224[理学—运筹学与控制论]