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

## TL;DR

This paper introduces a new second-order system for solving complex mathematical problems called inverse quasi-variational inequalities, with both theoretical and numerical validation.

## Contribution

The novel contribution is a second-order dynamical system for solving IQVIs with proven existence, uniqueness, and linear convergence properties.

## Key findings

- Existence and uniqueness of global solutions are established under standard conditions.
- A discrete-time formulation leads to a relaxed inertial projection algorithm with linear convergence.
- Numerical experiments validate the theoretical results and provide insights into IQVI problems.

## 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.