A geometric proximal gradient method for sparse least squares regression with probabilistic simplex constraint

Autor:	Xiao, Guiyun, Bai, Zheng-Jian
Rok vydání:	2021
Předmět:	Mathematics - Optimization and Control Mathematics - Numerical Analysis 65K05 90C25 90C26
Druh dokumentu:	Working Paper
Popis:	In this paper, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply the L1 regularization to the considered regression model. To find a sparse solution, we reformulate the 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, 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. Comment: 28 pages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2107.00809 Zobrazit plný text záznamu View this record from Arxiv