学术讲座【Customized Splitting Methods for Separable Convex Optimization】

时间：2014年12月26日 (星期五)上午9:00

地点：旗山校区理工北楼415多媒体教室

主讲：南京师范大学 韩德仁教授

主办：数学与计算机科学学院

专家简介：韩德仁，男，南京师范大学教授、博士生导师。2002年于南京大学获得博士位，2002年-2004年于新加坡国立大学SMA做博士后研究工作。主要从事大规模优化问题、变分不等式问题的数值方法的理论研究，以及优化和变分不等式问题在交通规划、磁共振成像中的应用研究。发表70余篇SCI论文，被引用600余次。文章发表在《Mathematical Programming》、《Numerische Mathematik》、 《SIAM Journal on Numerical Analysis》、《Mathematics of Computation》、《SIAM Journal on Imaging Sciences》、《Inverse Problems》、《Transportation Research Part B》等计算数学、运筹学重要期刊以及《IEEE Transaction on Signal Processing》、《Journal of Mathematical Imaging and Vision》等应用类期刊。

报告摘要：We consider applying the Douglas-Rachford splitting method (DRSM) to the convex minimization problem with linear constraints and a separable objective function. The dual application of DRSM has been well studied in the literature, resulting in the well known alternating direction method of multipliers (ADMM). In this paper, we show that the primal application of DRSM in combination with an appropriate decomposition can yield an ecient structure-exploiting algorithm for the model under consideration, whose subproblems could be easier than those of ADMM. Both the exact and inexact versions of this customized DRSM are studied; and their numerical eciency is demonstrated by some preliminary numerical results. We apply the algorithm to Dantzig Selector and compare it with some other splitting-type methods. Finally, some extensions are discussed.