题     目：An Efficient Proximal Difference-of-Convex Approach for Fitting the Sparse Envelope Model

报 告 人：陈亮 副教授

单     位：湖南大学

时     间：2022年11月9日10：00

地     点：腾讯390-850-080

摘 要：The sparse envelope model (SEM) is an efficient tool for the parameter estimation and the response variable selection in the multivariate linear regression. However, compared with the nice statistical properties that have been well established for the SEM, the corresponding algorithmic study is not sufficiently developed. In fact, the computational efficiency of solving the nonsmooth and nonconvex optimization problem arising from the SEM is crucial to the applicability of the SEM, since such a problem should be solved for many times, with different parameters for cross validation, even for fitting only a single instance. In this paper, we propose a highly efficient difference-of-convex (DC) approach for fitting the SEM. We first show how to construct the DC decomposition of the nonconvex optimization problem in the SEM, and then we incorporate the DC programming, together with the accelerated proximal gradient method (APG), to solve the problem. Numerical experiments are conducted, and the corresponding numerical results suggest that the proposed method is far superior to the existing block-wise coordinate descent approach.

报告人简介: 陈亮，湖南大学数学学院副教授，博士生导师，信息与计算科学系副主任，湖南省运筹学会秘书长。从事数值最优化方向的研究工作，在《Math. Program.》、《Math. Program. Comput.》、《Sci. China-Math.》等数学优化领域主流期刊发表论文10余篇，入选湖南省青年科技人才项目，主持国家重点研发计划青年科学家项目子课题、国家自然科学基金面上项目等科研项目。