报告人：中国科学院数学与系统科学研究院 娄有成 副研究员

报告题目：Convergence Properties of the Distributed Projected Subgradient Algorithm over General Graphs

报告摘要： Network balance plays an important role in the exact convergence of distributed optimization algorithms. A weight-balanced network requires that the in-degree of each node must be equal to its out-degree, which is, however, not always satisfied in practice. Different from most of existing works which focus on the design of distributed algorithms, we analyze convergence properties of a well-known distributed projected subgradient algorithm over time-varying general network graphs. We first show that the algorithm is not convergent in general. We then provide a necessary and sufficient condition on the cost functions–the intersection of optimal solution sets to all local optimization problems is nonempty–for the convergence of this algorithm under any uniformly jointly strongly connected graph sequence. Furthermore, we surprisingly find that the algorithm is convergent for any periodically switching graph sequence, and the converged solution minimizes a weighted sum of local cost functions, where the weights depend on the Perron vectors of some product matrices of the underlying periodically switching graphs. This work helps us understand impacts of the communication network on the convergence of distributed algorithms, and complements existing results from a different viewpoint.

报告人简介：娄有成，中国科学院数学与系统科学研究院副研究员。主要研究兴趣为分布式优化、行为金融、微观市场结构及其与复杂网络的交叉研究。在Journal of Economic Theory, Journal of Economic Dynamics and Control, IEEE Transactions on Automatic Control, Automatica等国际著名期刊上发表学术论文20余篇。入选2016年度香江学者计划，担任期刊International Journal of Economic Theory编委。

报告时间：2021年12月5日13：30-17：00

会议地点：腾讯会议（ID: 485 830 828）

组织者：任景莉，河南省大数据研究院大数据科学研究团队

联系人：陶亦文，联系电话：17719809695