Quantitative stability of two-stage stochastic linear variational inequality problems with fixed recourse

ABSTRACT

This paper focus on the quantitative stability of a class of two-stage stochastic linear variational inequality problems whose second stage problems are stochastic linear complementarity problems with fixed recourse matrix. Firstly, we discuss the existence of solutions to this two-stage stochastic problems and its perturbed problems. Then, by using the corresponding residual function, we derive the quantitative stability of this two-stage stochastic problem under Fortet-Mourier metric. Finally, we study the sample average approximation problem, and obtain the convergence of optimal solution sets under moderate assumptions.

Keywords:

• Two-stage stochastic variational inequality problem
• Residual function
• Quantitative stability analysis
• Sample average approximation
• Convergence analysis

Mathematics Subject Classification 2010:

• 90C15
• 90C33

Acknowledgments

The authors thank anonymous referees for their professional and helpful comments. This research was supported by the National Natural Science Foundation of China [grant numbers: 11571055, 11971078], the China Postdoctoral Science Foundation [grant number: 2019M653332] and the Natural Science Foundation of Chongqing [grant number: cstc2019jcyj-bshX0092].

Disclosure statement

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

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant numbers: 11571055,11971078], the China Postdoctoral Science Foundation [grant number: 2019M653332] and the Natural Science Foundation of Chongqing [grant number: cstc2019jcyj-bshX0092].