Sample average approximation method for a class of stochastic vector variational inequalities

Abstract

In the present paper, the expected-value (EV) reformulation of a class of stochastic vector variational inequalities (SVVI) is investigated. By using the regularized gap function, the EV reformulation of SVVI is transformed into a constrained optimization problem. Then a sample average approximation (SAA) method is proposed for solving the constrained optimization problem. Under suitable assumptions, the limiting behaviors of the optimal values and optimal solutions of the approximation problem are investigated. Finally, the rates of convergence in the different senses of optimal solutions for sample average approximation problem are discussed under the error bound condition.

Keywords:

• Stochastic vector variational inequality
• regularized gap function
• sample average approximation
• convergence

2020 Mathematics Subject Classifications:

• 90C15
• 90C33

Disclosure statement

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

Additional information

Funding

The authors are grateful to the editor and referee for their valuable comments and suggestions. This work was partially supported by National Natural Science Foundation of China (No. 11961006), Guangxi Science and Technology Plan Project (No. guikeAD22035021), Guangxi Natural Science Foundation (No. 2020GXNSFAA159100) and Innovation Project of Guangxi Graduate Education (gxun-chxs2021055).