具有概率简单度限制的稀薄最小平方回归的几何准度梯度法 (A geometric proximal gradient method for sparse least squares regression with probabilistic simplex constraint)

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.

翻译：在本文中,我们用概率简单x限制来考虑稀有的最小方块回归问题。由于概率简单x限制, 我们无法将L1正规化适用于考虑的回归模式。为了找到一个稀疏的解决办法, 我们重新将最小方块回归问题重新表述为单位范围上的非曲线和非移动L1 常规最小化的最小化问题。然后我们提出一个几何准轴梯度方法来解决常规化问题, 从而获得对每个所涉子问题的全球解决方案的明确表达。所提议方法的全球趋同是在一些轻度假设下确立的。报告了一些数字结果, 以说明拟议算法的有效性。