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香港理工大学 杨晓琪教授:Group sparse optimization via $ell_{p,q}$ regularization

([西财新闻] 发布于 :2018-06-11 )

光华讲坛——社会名流与企业家论坛第4999

 

Group sparse optimization via $\ell_{p,q}$ regularization

主讲人香港理工大学 杨晓琪教授

主持人经济数学学院   孟开文

2018613日(星期三)上午10:00-1100

西南财经大学柳林校区通博楼B412

主办单位:经济数学学院  科研处

 

主讲人简介:

Academic qualifications:  B.Sc., Chongqing Jianzhu University, 1982, M.Sc., Chinese Academy of Science, 1987, and Ph.D., University of New South Wales, 1994

Present academic position: May 2005 -, Professor; Hong Kong Polytechnic University

Previous relevant research work: duality and penalty function theory and methods for nonlinear constrained programming problems, semi-definite programs, and nonconvex multiple objective optimization problems with applications to portfolio selection and American option pricing.

Publications records: 3 research monographs, over 220 refereed journal papers, 3 edited books and 7 edited special journal issues. PhD theses supervised as Chief Supervisor: 10 PhD graduates and 2 current PhD students.

内容提要:

In this paper, we investigate a group sparse optimization problem via $\ell_{p,q}$ regularization in three aspects: theory, algorithm and application. In the theoretical aspect, by introducing a notion of group restricted eigenvalue condition, we establish an oracle property and a global recovery bound of order $O(\lambda^\frac{2}{2-q})$ for any point in a level set of the $\ell_{p,q}$ regularization problem, and by  virtue of modern variational analysis techniques, we also provide a local analysis of recovery bound of order $O(\lambda^2)$ for a path of local minima. In the algorithmic aspect, we apply the well-known proximal gradient method to solve the $\ell_{p,q}$ regularization problems, either by analytically solving some specific $\ell_{p,q}$ regularization subproblems,  or by using the Newton method to solve general $\ell_{p,q}$ regularization subproblems.

In particular, we establish a local linear convergence rate of the proximal gradient method for solving the $\ell_{1,q}$ regularization problem under some mild conditions and by first proving a second-order growth condition. As a consequence, the local linear convergence rate of proximal gradient method for solving the usual $\ell_{q}$ regularization problem ($0<q<1$) is obtained. Finally in the aspect of application, we present some numerical results on both the simulated data and the real data in gene transcriptional regulation.

 


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