An Inexact Variance-Reduced Method for Stochastic Quasi-Variational Inequality Problems with an Application In Healthcare

Zeinab Alizadeh, Brianna M. Otero, Afrooz Jalilzadeh

Abstract: This paper is focused on a stochastic quasi-variational inequality (SQVI) problem with a continuous and strongly-monotone mapping over a closed and convex set where the projection onto the constraint set may not be easy to compute. We present an inexact variance reduced stochastic scheme to solve SQVI problems and analyzed its convergence rate and oracle complexity. A linear rate of convergence is obtained by progressively increasing sample-size and approximating the projection operator. Moreover, we show how a competition among blood donation organizations can be modeled as an SQVI and we provide some preliminary simulation results to validate our findings.