向量变分不等式的高阶可微性与灵敏性  

High-order differentiability and sensitivity of vector variational inequalities

作　　者：马权禄 薛小维 MA Quanlu;XUE Xiaowei(College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China;College of Mathematics and Big Data,Chongqing University of Arts and Sciences,Chongqing 402160,China)

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：《山东大学学报(理学版)》2025年第2期105-113,共9页Journal of Shandong University(Natural Science)

基　　金：重庆市教委科学技术研究资助项目(KJQN20220134);重庆市研究生联合培养基地建设资助项目(JDLHPYJD2021016);重庆市高校创新研究群体资助项目(CXQT21021)。

摘　　要：研究向量变分不等式和弱向量变分不等式两类问题的高阶可微性与灵敏性。介绍了相依锥、高阶切集等的基本定义,研究了与向量变分不等式密切相关的一类集值映射的高阶微分性质,得到了其高阶导数的精确计算公式。通过讨论集值映射与其剖面映射二者高阶导数之间的关系,得到了向量变分不等式的高阶可微性与灵敏性。The paper studies the higher-order differentiability and sensitivity of vector variational inequalities and weak vector variational inequalities.The basic definitions of contingent cones,higher-order tangent sets are introduced.The higher-order differential properties of a class of set-valued maps closely related to vector variational inequalities are studied,and the accurate calculation formula of its higher-order derivatives is obtained.By discussing the relationship between the higher-order derivatives of set-valued mapping and its profile mapping,the higher-order differentiability and sensitivity of vector variational inequalities are obtained.

关 键 词：向量变分不等式 高阶切集 相依导数 灵敏性 

分 类 号：O224[理学—运筹学与控制论]