A second-order dynamical system for solving inverse quasi-variational inequalities and its application.

Abstract

In this paper, we focus on a second-order dynamical system designed to solve inverse quasi-variational inequalities (IQVIs) in Hilbert spaces, focusing on strongly monotone operators under Lipschitz continuity assumptions. This study establishes the existence and uniqueness of strong global solutions under standard conditions, ensuring the robustness of the proposed system. Furthermore, we derive a discrete-time formulation of the dynamical system, which leads to a relaxed inertial projection algorithm that achieves linear convergence under suitable parameter conditions. Beyond theoretical analysis, stability is verified using a Lyapunov function. Finally, numerical experiments confirm the theoretical results and provide deeper insight into inverse quasi-variational inequality problems within the framework of dynamical systems.