题目：A Geometric Proximal Gradient Method for Sparse Least Squares Regression with Probabilistic Simplex Constraint
报告人：白正简 教授 单位： 厦门大学 数学科学学院
时 间：2022年4月29日（周五）上午 9:00-10:00
腾讯会议：383-738-106
报告人及报告内容简介：
白正简，厦门大学教授、博士生导师。2004年博士毕业于香港中文大学，曾在新加坡国立大学和意大利Insubria 大学作博士后和访问学者。主要研究方向为数值代数、特征值问题及其逆问题、矩阵流形及其在数据科学中的应用等。曾主持国家自然科学基金面上项目和福建省杰出青年基金。在SIAM系列, Numer. Math., Inverse Problems等本学科主流期刊上发表学术论文40余篇。曾获得2009年度福建省科学技术奖二等奖和2010年度“教育部新世纪优秀人才支持计划”入选者。
Abstract:
In this talk, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply directly the L1-regularization to the considered regression model. To find a sparse solution, we reformulate the sparse least squares regression problem as a nonconvex and nonsmooth L1-regularized minimization problem over the unit sphere. Then we propose a geometric proximal gradient method for solving the regularized problem with a varied regularized parameter, where the explicit expression of the global solution to every involved subproblem is obtained. The global convergence of the proposed method is established under some mild assumptions. Some numerical results are reported to illustrate the effectiveness of the proposed algorithm.