题    目：Convergence Analysis of Generalized ADMM with Majorization for Linearly Constrained Composite Convex Optimization

报告人：李红武

单    位：南阳师范学院

时    间：7月14日9:00

地    点：腾讯会议333 6063 3863

摘要：The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of "nonsmooth + quadratic". However, in the case of non-quadratic (but smooth), this method may fail unless the favorable structure of 'nonsmooth + smooth' is no longer used. This paper aims to remedy this defect by using a majorized technique to approximate the augmented Lagrangian function, so that the corresponding subprobllem can be decomposed into some smaller problems and then solved separately. Furthermore, the recent symmetric Gauss-Seidel (sGS) decomposition theorem guarantees the equivalence between the bigger subproblem and these smaller ones. This paper focuses on convergence analysis, that is, we prove that the sequence generated by the proposed method converges globally to a Karush-Kuhn-Tucker point of the considered problem. Finally, we do some numerical experiments on a kind of simulated convex composite optimization problems which illustrate that the proposed method is more efficient than its compared ones.

报告人简介：李红武，男，北京工业大学在读博士，南阳师范学院副教授，主要从事优化理论及算法研究，先后主持河南省高等教育教改项目1项，省精品在线开放课程1门，参与完成教育部人文社科规划项目1项、河南省教学成果二等奖1项，在国内外核心期刊发表学术论文10余篇。