Uncertain Variational Inequalities Based on Chance Constraints

Qiqiong Chen (), Xuhuan Wang (), Xiaoliang Feng () and Hong-Kun Xu ()
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Qiqiong Chen: Zhejiang Sci-Tech University
Xuhuan Wang: Pingxiang University
Xiaoliang Feng: Chuzhou University
Hong-Kun Xu: Hangzhou Dianzi University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 1, No 4, 17 pages

Abstract: 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.

Keywords: Gap function; Variational inequality; Chance constraint; Uncertain variable; 90B20; 90C33; 90C70 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02668-7

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