报告人: 孟开文教授（西南交通大学）
报告时间：2017年6月27日（星期二）下午4:30-5:30
报告地点：维格堂119
报告摘要：
In this paper, we investigate a group sparse optimization problem vialp,qregularization in three aspects: theory, algorithm and application. Inthe theoretical aspect, by introducing a notion of group restricted eigenvaluecondition, we establish an oracle property and a global recovery bound forany point in a level set of the lp,q regularization problem, and by virtue of modern variational analysis techniques, we also provide a localanalysis of recovery bound for a path of local minima. In the algorithmicaspect, we apply the well-known proximal gradient method to solve the lp,qregularization problems, either by analytically solving some specific lp,qregularizationsubproblems, or by using the Newton method to solve generallp,qregularization subproblems. In particular, we establish a local linearconvergence rate of the proximal gradient method for solving the l1,qregularization problem under some mild conditions and by first proving asecond-order growth condition. As a consequence, the local linearconvergence rate of proximal gradient method for solving the usual lqregularization problem .
孟开文老师简介：
Dr. Kaiwen Meng is an Associate Professor at School of Economics andManagement, Southwest Jiaotong University. He works on finite dimensionaloptimization problems, focussing on decisions with multiple objectives,penalty function theory, methods and applications, generalized polyhedratheory and applications, and portfolioselection theory. Kaiwen receivedhis Ph.D. in applied mathematics from the Hong Kong Polytechnic Universityin 2011. He has published around 15 papers in international journals,including SIAM Journal on Optimization, Operations Research, and Journalof Machine Learning Research.