一类带MCP函数正则化问题的稳定性研究

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

本文研究一类带极大极小凹惩罚(MCP)函数正则化问题,该模型由二次可微的损失函数和MCP函数组成。首先我们研究了MCP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,得到带MCP正则化问题目标函数次微分图像导数。最后,利用该图像导数表达式分别建立了该正则化问题次微分强度量次正则的充分条件和充要条件。

In this paper, we study a class of regularization problems with the minimax concave penalty (MCP) function, which consists of a twice differentiable loss function and the MCP penalty function. First, we study the prox-regular subdifferential and limiting subdifferential of the MCP penalty function. Next, we obtain the graphical derivative of regularization problems with the MCP penalty function by using the subdifferential expression. Finally, we use the graphical derivative to establish a sufficient condition, a sufficient and necessary condition for the strong metric subregularity of subdifferential of the regularization problems, respectively.