应数学系马坚伟教授邀请，香港浸会大学数学系袁晓明副教授访问我校，并做交替方向优化算法相关的学术报告。袁教授在算子分裂凸优化领域做出重要贡献，发表论文约50篇，其中在SIAM Journal 和 Mathematical Programming上发表20余篇。欢迎广大师生参加。

题目：On the Extension of ADMM for Separable Convex Programming and Beyond: From Variational Inequality Perspective

报告人：Xiaoming Yuan, Associate Professor, Department of Mathematics, Hongkong Baptist University

时间：2013.12.26, 16:00-17:00

地点：一区新活动中心326

摘要：The alternating direction method of multipliers (ADMM) is now widely used in many fields. It is strongly desired and practically used to extend ADMM naturally to the case of convex programming where its objective function is the sum of three convex functions without coupled variables. The direct extension of ADMM, however, is not necessarily convergent even though it performs very well for many applications. We propose a prototype algorithm in form of variational inequality for the separable convex minimization model with three uncoupled objective functions. The extended ADMM and some benchmarks in the literature such as the augmented Lagrangian method (ALM) and the original ADMM can all be recovered by this prototype algorithm. A unified and easily checkable condition to ensure the convergence of this prototype algorithm is given. To make this prototype algorithm specific, we propose a class of ADMM-based algorithms that preserve completely the numerical advantages of the extended ADMM. Theoretically, we show the contraction property of the prototype algorithm, and consequently establish its global convergence and worst-case convergence rates measured by iteration complexity. Numerically, an important feature of this new class of algorithms is that they could be even faster than the extended ADMM for some applications.

专家简介：Xiaoming Yuan received B.Sc and M.Phil degrees at Nanjing University; and PhD degree at City University of Hong Kong, all majoring in Mathematics. He had worked at University of Victoria, Shanghai Jiao Tong University and University of British Columbia Okanagan before joined Hong Kong Baptist University. His research focuses on numerical optimization (both algorithmic design and theory), with particular interests in variational inequalities and complementarity problems, sparse and low-rank optimization, first-order methods for large-scale convex programming problems, and image processing. He published more than 20 papers at SIAM Journal and Mathematical Programming.

http://www.math.hkbu.edu.hk/~xmyuan/