A Third Order Dynamical System for Mixed Variational Inequalities

TL;DR

This paper introduces a third order dynamical system approach for solving mixed variational inequalities, demonstrating stability and convergence properties under mild conditions, and extending potential applications.

Contribution

It proposes a novel third order resolvent dynamical system for mixed variational inequalities, with new convergence and stability results under monotonicity assumptions.

Findings

Established global asymptotic stability of the system

Proved exponential convergence rates

Applicable to a broad class of variational inequalities

Abstract

In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates of convergences require only the monotonicity for mixed variational inequalities under some mild conditions. We establish the global asymptotically and exponentially stability of the solution of the resolvent dynamical system for monotone operators. Ideas and techniques of this paper may be extended for other classes of variational inequalities and equilibrium problems.