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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (2): 105-113.doi: 10.6040/j.issn.1671-9352.0.2023.400

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向量变分不等式的高阶可微性与灵敏性

马权禄1,薛小维2*   

  1. 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
  • 出版日期:2025-02-20 发布日期:2025-02-14
  • 通讯作者: 薛小维(1982— ), 男, 副教授, 硕士生导师, 博士, 研究方向为复杂系统优化与决策. E-mail:xuexw1@126.com
  • 作者简介:马权禄(1998— ),男,硕士研究生,研究方向为复杂系统优化与决策. E-mail:2990494687@qq.com
  • 基金资助:
    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)

High-order differentiability and sensitivity of vector variational inequalities

MA Quanlu1, XUE Xiaowei2*   

  1. 1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China;
    2. College of Mathematics and Big Data, Chongqing University of Arts and Sciences, Chongqing 402160, China
  • Online:2025-02-20 Published:2025-02-14

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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。

关键词: 向量变分不等式, 高阶切集, 相依导数, 灵敏性

Abstract: 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.

Key words: vector variational inequality, higher-order tangent sets, contingent derivative, sensitivity

中图分类号: 

  • O224
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