Deterministic Bi-Criteria Model for Solving Stochastic Mixed Vector Variational Inequality Problems

Meiju Luo (), Menghan Du and Yue Zhang
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Meiju Luo: School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China
Menghan Du: School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China
Yue Zhang: School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China

Mathematics, 2023, vol. 11, issue 15, 1-19

Abstract: In this paper, we consider stochastic mixed vector variational inequality problems. Firstly, we present an equivalent form for the stochastic mixed vector variational inequality problems. Secondly, we present a deterministic bi-criteria model for giving the reasonable resolution of the stochastic mixed vector variational inequality problems and further propose the approximation problem for solving the given deterministic model by employing the smoothing technique and the sample average approximation method. Thirdly, we obtain the convergence analysis for the proposed approximation problem while the sample space is compact. Finally, we propose a compact approximation method when the sample space is not a compact set and provide the corresponding convergence results.

Keywords: stochastic; mixed vector variational inequality; deterministic bi-criteria model; sample average approximation; compact approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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