一类变分包含正则间隙函数的可微性与解的局部唯一性  

Differentiability of regularized gap functions for a kind of variational inclusions and local uniqueness of solutions

作　　者：宋文[1] Wen Song

机构地区：[1]哈尔滨师范大学数学科学学院,哈尔滨150025

出　　处：《中国科学：数学》2020年第12期1869-1890,共22页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11871182)资助项目。

摘　　要：本文借助于邻近正则函数的Moreau包络及其邻近映射的性质,建立一类非凸变分包含正则间隙函数及其解映射的Lipschitz连续性和可微性;利用二阶变分分析理论得到了变分包含解的局部唯一性及关于参数的连续性.同时也概述了变分不等式和优化问题正则间隙函数的发展过程及邻近正则函数的变分性质.In this paper, we mainly explore continuity and differentiability properties of regularized gap functions for a kind of nonconvex variational inclusions and its associated solution mapping by making use of the properties of the Moreau envelope functions of the prox-regular function and its proximal mapping. By applying the second order variational analysis, we obtain the local uniqueness and continuity on parameters of solutions for the variational inclusions. We also survey the developing process of regularized gap functions for the variational inequality and optimization, and variational properties of prox-regular functions.

关 键 词：正则间隙函数 Moreau包络 邻近映射 邻近正则 上图可微 

分 类 号：O178[理学—数学]