一类带对数罚函数的正则化问题的强度量次正则研究  

Study on the Strong Metric Subregularity for a Class of Regularization Problems with Logarithmic Penalty Functions

作　　者：冯盼盼 廖春美 李明华[2] FENG Panpan;LIAO Chunmei;LI Minghua(School of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074;College of Mathematics and Big Data,Chongqing University of Arts and Sciences,Chongqing 402160)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074 [2]重庆文理学院数学与大数据学院,重庆402160

出　　处：《系统科学与数学》2025年第1期253-261,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12271072);重庆市自然科学基金(CSTB2022NSCQ-MSX0409,CSTB2022NSCQ-MSX0406,CQ-NCAM-2021-02);重庆市教育委员会科技项目(KJZD-M202201303,KJQN202201349)资助课题。

摘　　要：文章研究一类带对数罚函数的正则化问题,该模型的目标函数由损失函数和对数罚函数组成,其中损失函数是二次可微函数,对数罚函数是一个非凸函数.首先,研究对数罚函数的邻近次微分和极限次微分,然后,利用该次微分表达式和图像导数的运算法则,得到该问题目标函数的次微分图像导数,最后,利用该图像导数表达式分别建立了该正则化问题的强度量次正则的一个充分条件和充要条件.This paper studies a class of regularization problems with a logarithmic penalty function.The objective function consists of a loss function and a logarithmic penalty function,where the loss function is a twice differentiable function,and the logarithmic penalty function is a non-convex function.We first study the prox-regular subdifferential and limiting subdifferential of the logarithmic penalty function,and then use the subdifferential expression to obtain the graphical derivative of the ob-jective function,and finally,we use the graphical derivative to establish a suficient condition,and a sufficient and necessary condition for the strong metric subregularity of the problem,respectively.

关 键 词：次微分 图像导数 强度量次正则性 对数罚函数正则化问题 

分 类 号：O172.1[理学—数学]