摘要
文章研究了存在通信时延情况下的多个体分布式次梯度优化算法。通过系统扩维,将存在通信时延情形的优化问题转化为无时延情形的优化问题,同时所得通信网络对应的邻接矩阵是一个所有主对角元素不必全为正数的随机矩阵,从而弱化了已有文献关于邻接矩阵的若干假定;进而利用不可逆Markov链的相关结论,证明了只要通信时延有上界,则优化算法最终仍然收敛,并发现通信时延会造成较大的迭代误差;最后通过仿真算例验证了文中算法的有效性。
The distributed subgradient method for multi-agent optimization problem with communication delays is studied. By augmenting delay nodes in communication network, the optimization problem with communication delays is converted into the optimization problem without communication delays. Meanwhile, the corresponding adjacency matrix associated with the augmented communication network may be stochastic and all its diagonal entries are not necessarily positive. Thus, some typical requirements for the adjacency matrix in existing literature are weakened. Then based on the related result of non-reversible Markov theory, it is proved that the convergence of the proposed optimization algorithm can still be guaranteed provided that communication delays have upper bound. The obtained results show that communication delays induce more updated errors. Finally, an example is given to demonstrate the effectiveness of the presented optimization algorithm.
出处
《合肥工业大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第5期559-565,共7页
Journal of Hefei University of Technology：Natural Science
基金
国家自然科学基金资助项目(61073102
61170172)
关键词
分布式凸优化
通信时延
次梯度算法
多个体系统
随机矩阵
distributed convex optimization
communication delay
subgradient method
multi-agent system stochastic matrix
作者简介
刘军（1987-），男，湖北荆州人，安徽理工大学硕士生
李德权（1973～），男，安徽肥东人，博士，安徽理工大学教授，硕士生导师
