Convergence Analysis of Non-Strongly-Monotone Stochastic Quasi-Variational Inequalities

• DOI: 10.48550/arxiv.2401.03076
• Publication Date: 2024-01-01
• Authors: Zeinab Alizadeh; Afrooz Jalilzadeh
• Keywords: Saddle point; Variational analysis; Saddle

While Variational Inequality (VI) is a well-established mathematical framework that subsumes Nash equilibrium and saddle-point problems, less known about its extension, Quasi-Variational Inequalities (QVI). QVI allows for cases where the constraint set changes as decision variable varies allowing more versatile setting. In this paper, we propose extra-gradient gradient-based methods solving class of monotone Stochastic (SQVI) establish rigorous convergence rate analysis these methods. Our approach not only advances theoretical understanding SQVI but also demonstrates practical applicability. Specifically, highlight effectiveness in reformulating problems such generalized Equilibrium, bilevel optimization, with coupling constraints.