摘要
本文考虑无约束组稀疏回归问题,其损失函数为凸函数,正则项为MCP(minimax concave penalty),主要刻画该问题的两类稳定点。首先,给出d-稳定点以及critical点的具体刻画,并且证明了这两类稳定点的关系;其次,分析d-稳定点与问题局部解的关系;最后,证明了该模型的下界性质。
In this paper,we focus on the group sparse problem,where the loss function is convex,and the penalty term is defined by the minimax concave penalty.We discuss two kinds of stationary points of the problem.First,we provide concrete description for the d-stationary point and the critical point of the nonconvex regular group sparse problem,and analyze the relation of d-stationary point with critical point.Furthermore,we show that a point is a local minimizer of the relaxation problem,then it is a d-stationary point.What’s more,we obtain the lower bound property of the problem.
作者
唐琦
彭定涛
TANG Qi;PENG Dingtao(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China)
出处
《贵州大学学报（自然科学版）》
2020年第4期10-15,共6页
Journal of Guizhou University:Natural Sciences
基金
国家自然科学基金资助项目(11861020)
贵州省高层次留学人才创新创业择优资助重点项目([2018]03)
贵州省科技计划资助项目([2018]5781)
贵州省青年科技人才成长资助项目([2018]121)。
