A Geometric Proximal Gradient Method for Sparse Least Squares Regression with Probabilistic Simplex Constraint

讲座时间 Datetime: 2022年6月17日，星期五，  9:30-11:30

地点 Venue: 腾讯线上会议：496633401

 主持人 Host：刘海峰

报告人 Speaker:白正简

单位 Affiliation:厦门大学

报告摘要 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.