Some Recent Developments of Alternating Directions Method of Multipliers
何炳生
Professor
Department of Mathematics, NanJing University
Abstract: The alternating directions method of multipliers (ADMM) is well recognized as a powerful approach to tackle a two-block convex minimization model whose objective function is separable as two functions without coupled variables. However, when ADMM is directly extended to a three-block convex minimization model, the convergence is not guaranteed. In this talk, we will review some recent developments on ADMM, including constructing more efficient ADMM-based schemes for two-block models, and modifying slightly the direct extension of ADMM and proposing ADMM-based schemes for three-block models. We show the contraction property, prove the global convergence and establish the worst-case convergence rate measured by the iteration complexity. All the analysis is conducted in variational inequality contexts. The proposed methods can be easily extended to models with more than three blocks.
Bio: 何炳生，南京大学数学系教授，博士研究生导师。1966年读完高中，南京大学数学系 77 级学生，本科毕业后公派去联邦德国留学，取得博士学位后于 1987年开始在南京大学数学系工作。1997年晋升为教授。江苏省有突出贡献的中青年专家，享受国务院特殊津贴。2000年获美国科技情报研究所的经典引文奖, 2001年独立获得江苏省科技进步一等奖。2014年获得中国运筹学会《运筹研究奖》。何炳生教授长期从事结构型单调变分不等式和凸优化方法的研究，发表论文 80 余篇。代表性论文发表在《Mathematical Programming》及《SIAM》的系列期刊上。根据分解降低难度，整合把握方向的原则，提出的系列方法都纳入一个简单的统一框架，被国际著名学者认为极大地简化了 Primal-dual 方法的收敛性证明。部分成果被包括多位美国两院院士和《世界数学家大会》大会报告人为作者的论文大篇幅引用。