Second order continuous and discrete dynamical systems for solving inverse quasi-variational inequalities

TL;DR

This paper introduces a second-order dynamical system and its discretization for efficiently solving inverse quasi-variational inequalities, with proven exponential and linear convergence, validated through numerical experiments.

Contribution

The paper develops a novel second-order dynamical system and a discretized algorithm for inverse quasi-variational inequalities, demonstrating improved convergence properties.

Findings

Exponential convergence of the continuous dynamical system.

Linear convergence of the discretized algorithm.

Numerical experiments validating theoretical results.

Abstract

In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse quasi-variational inequality, under the assumptions of Lipschitz continuity and strong monotonicity. Next, we discretize the proposed dynamical system to develop an algorithm, and prove that the iterations converge linearly to the unique solution of the inverse quasi-variational inequality. Finally, we present numerical experiments and applications to validate the theoretical results and compare the performance with existing methods.