A Second-Order Dynamical System for Solving Generalized Inverse Mixed Variational Inequality problems

TL;DR

This paper introduces a second-order dynamical system and an inertial projection algorithm for solving generalized inverse mixed variational inequality problems, demonstrating their convergence and effectiveness through theoretical analysis and numerical experiments.

Contribution

It proposes a novel second-order dynamical system and an inertial projection algorithm with proven convergence for GIMVIPs, advancing solution methods for these problems.

Findings

The dynamical system has a unique solution that converges exponentially.

The discrete algorithm achieves linear convergence under proper parameters.

Numerical experiments confirm the method's effectiveness in solving GIMVIPs.

Abstract

In this paper, we study a class of generalized inverse mixed variational inequality problems (GIMVIPs). We propose a novel projection-based second-order time-varying dynamical system for solving GIMVIPs. Under the assumptions that the underlying operators are strongly monotone and Lipschitz continuous, we establish the existence and uniqueness of solution trajectories and prove their global exponential convergence to the unique solution of the GIMVIP. Furthermore, a discrete-time realization of the continuous dynamical system is developed, resulting in an inertial projection algorithm. We show that the proposed algorithm achieves linear convergence under suitable choices of parameters. Finally, numerical experiments are presented to illustrate the effectiveness and convergence behavior of the proposed method in solving GIMVIPs.