报告地点：线上报告
邀请人：孙海琳教授
摘要：In this talk, I will first introduce a unified algorithmic framework, which is a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based proximal alternating direction methods of multipliers (ADMMs), for solving convex composite optimization problems. Specifically, the majorized augmented Lagrangian functions, the indefinite proximal terms, the inexact symmetric Gauss-Seidel decomposition theorem, the tolerance criteria of approximately solving the subproblems, and the large dual step-lengths, are all incorporated. Then, I will show that an (inexact) symmetric Gauss-Seidel based majorized multi-block ADMM is equivalent to an inexact proximal augmented Lagrangian method, which not only provides new perspectives for understanding ADMMs but also supplies meaningful guidelines on implementing them. Finally, I will illustrate some numerical strategies that we exploited to tackle the computational burdens that we were confronted with when applying the proposed algorithms to solving the large-scale problems.
Main References：
[1] Liang Chen, Defeng Sun, and Kim-Chuan Toh: An efficient inexact symmetric Gauss-Seidel based majorized ADMM for high-dimensional convex composite conic programming, Mathematical Programming, 2017, 161(1): 237—270
[2] Liang Chen, Defeng Sun, Kim-Chuan Toh, and Ning Zhang: A unified algorithmic framework of symmetric Gauss-Seidel decomposition based proximal ADMMs for convex composite programming, Journal of Computational Mathematics, 2019, 37: 739—757
[3] Liang Chen, Xudong Li, Defeng Sun, and Kim-Chuan Toh: On the equivalence of inexact proximal ALM and ADMM for a class of convex composite programming, Mathematical Programming, online, DOI: 10.1007/s10107-019-01423-x
个人简介：陈亮博士目前是湖南大学数学学院助理教授。他于2009年在湖南大学数学学院获学士学位，2016年获博士学位，在博士期间在新加波国立大学访问。2017-2019年在香港理工大学进行博士后研究。目前在Mathematical Programming等优化领域著名期刊发表论文9篇，主持国家自然科学基金和湖南省自然科学基金各一项，担任湖南省运筹学会理事。