Quantitative stability for a class of stochastic vector linear variational inequalities

Abstract

This paper considers the expected value (for short, EV) formulation for a class of stochastic vector linear variational inequalities (for short, SVLVI). We first discuss the existence of solutions to both the original problem and its perturbed problem. Then, under suitable probability metrics, we derive the quantitative stability of SVLVI. Finally, we study the discrete approximation problem, and obtain the rates of convergence of optimal solution sets under different assumptions.

Keywords:

• Stochastic vector linear variational inequalities
• probability metrics
• quantitative stability
• discrete approximation
• convergence properties

2020 Mathematics Subject Classifications:

• 90C15
• 90C33

Acknowledgments

The authors are grateful to the editor and anonymous referees for their valuable comments and constructive suggestions, which helped to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of Jianxun Liu was supported by the Scientific Research Project of Guangxi Minzu University [grant number 2021KJQD05], the Guangxi Science and Technology Plan Project [grant number guikeAD22035021] and the Basic Ability Enhancement Program for Young and Middle-aged Teachers of Guangxi [grant number 2022KY0163]. The work of Yong Zhao was supported by the National Natural Science Foundation of China [grant numbers 12001072, 12271067], the NSFC-RGC (Hong Kong) Joint Research Program [grant number 12261160365] and the Chongqing Natural Science Foundation [grant numbers cstc2019jcyj-zdxmX0016, CSTB2022NSCQ-MSX1318].