分布式优化: 算法设计和收敛性分析

Distributed optimization: algorithm design and convergence analysis

中文关键词  分布式优化  约束  (次)梯度法  Nash均衡

英文关键词  distributed optimization  constraints  (sub-)gradient method  Nash equilibrium

中文摘要

      近年来, 随着高科技的蓬勃发展, 特别是云计算和大数据等新兴领域的出现, 分布式优化理论和应用得到了越来越多的重视, 并逐渐渗透到科学研究、工程应用和社会生活的各个方面, 分布式优化是通过多智能体之间的合作协调有效地实现优化的任务, 可用来解决许多集中式算法难以胜任的大规模复杂的优化问题. 如今如何设计出有效的分布式优化算法并对其进行收敛性和复杂性的分析成了优化研究的主要任务之一. 与集中式算法的主要区别在于分布式算法还不得不考虑通讯和协调在优化中起到的重要作用. 本文集中讨论了近年来分布式优化研究中的一些典型热门的研究问题, 从一个侧面介绍了包括无约束优化、带约束优化、以及分布式博弈等方向的部分最新成果. 同时也比较详尽地论述了笔者最近的相关研究成果. 最后, 本文简要地对分布式优化的研究和应用前景进行了展望.

英文摘要

      In recent years, theoretical and practical researchers on distributed optimization are spending more and more efforts to meet the challenge of rapid development of high techniques, particularly the new areas such as the cloud computation and big data sets. Moreover, distributed optimization is increasingly applied to many fields such as scientific researches, engineering applications, and social activities. Distributed optimization considers effective coordination between multiple agents, and can be applied to many large-scale complicated optimization problems that are difficult to be solved by centralized algorithms. How to design an effective distributed optimization algorithm with convergence and limited complexity is one of the most important objectives in optimization research. Being different from the centralized algorithm, a distributed algorithm has to take into account the communication and coordination in the process of optimization. In this paper, we focus on some standard hot topics in recent distributed optimization problems, such as the unconstrained optimization, constrained optimization, and distributed game. On those topics we make a brief survey of recent achievements including some of our research results, and point out prospects for further studies in theoretical research or practical applications.