时延情形下分布式 Push －sum 次梯度优化算法的研究

摘要

针对多个体系统在个体间进行信息交换时发生接收信息滞后，存在通信时延，影响优化算法的收敛速度的问题，提出一种时延情形下的分布式Push－sum次梯度优化算法，该方法在权矩阵不具有正对角线元素时仍适用，并应用系统扩维的方法将有时延优化问题转化为无时延优化问题。在时延和次梯度有界且有向切换网络周期强连通的条件下，证明了所提出的分布式Push－sum次梯度优化算法的收敛性。研究表明：存在通信时延时的算法收敛速度比无时延时的收敛速度要慢，并具有较大的收敛误差。最后，通过数值仿真验证了研究的结论。%The distributed optimization problem in directed switching networks with time-varying delay commu-nication among the agents was studied.Due to delay may happen when agents communicate with each other in the multi-agent system, this paper proposes a distributed Push-sum subgradient optimization algorithm in the context of communication delays, which will affect the convergence rate of optimization algorithm.Then based on state augmentation method, the analysis is carried out by reducing the optimization problem with delays to a prob-lem without delays and this algorithm does not require the diagonal elements of the adjacency matrix are all posi-tive.Under the assumptions that communication delays and the subgradients are bounded, and the switching di-rected networks are periodically strongly connected, we prove that the convergence of the proposed distributed Push-sum subgradient optimization algorithm.It is shown that the convergence rate in the case of communica-tion delays is slower than that without communication delays, and meanwhile the proposed algorithm may bring out large convergence error.Finally, the conclusion is verified by numerical simulation.