JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (2): 105-113.doi: 10.6040/j.issn.1671-9352.0.2023.400

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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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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

CLC Number: 

  • O224
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