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Uncertain Variational Inequalities Based on Chance Constraints

Author

Listed:
  • Qiqiong Chen

    (Zhejiang Sci-Tech University)

  • Xuhuan Wang

    (Pingxiang University)

  • Xiaoliang Feng

    (Chuzhou University)

  • Hong-Kun Xu

    (Hangzhou Dianzi University)

Abstract

This paper is mainly concerned with a class of variational inequality whose underlying set is defined by chance constraints in finite-dimensional Euclidean spaces. To solve it, the inverse uncertainty distribution function in uncertainty theory is used to convert the underlying set into a parameter-dependent set under some conditions, say $$\alpha $$ α -dependent set, where $$\alpha \in (0,1]$$ α ∈ ( 0 , 1 ] is a confidence level. Then an $$\alpha $$ α -dependent gap function based on the $$\alpha $$ α -dependent set is brought to light and an equivalence between it and the solution to the variational inequality is unveiled. Furthermore, a descent algorithm (exact line search) is executed to find the solution to the gap function which is also a solution to the variational inequality under investigation. As to close the paper, a traffic network equilibrium problem, a special case of Nash equilibrium problem, is applied to demonstrate the method in detail.

Suggested Citation

  • Qiqiong Chen & Xuhuan Wang & Xiaoliang Feng & Hong-Kun Xu, 2025. "Uncertain Variational Inequalities Based on Chance Constraints," Journal of Optimization Theory and Applications, Springer, vol. 206(1), pages 1-17, July.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:1:d:10.1007_s10957-025-02668-7
    DOI: 10.1007/s10957-025-02668-7
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    References listed on IDEAS

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