Second-order dynamical systems with a smoothing effect for solving paramonotone variational inequalities

TL;DR

This paper introduces a second-order dynamical system with a smoothing effect to solve paramonotone variational inequalities, proving convergence and developing an iterative method with numerical validation.

Contribution

It presents a novel second-order dynamical system with smoothing for variational inequalities, extending and improving existing convergence results.

Findings

Trajectories converge to solutions under standard assumptions

Discretized system yields an effective inertial projection method

Numerical examples confirm theoretical convergence and effectiveness

Abstract

In this paper, we propose a second-order dynamical system with a smoothing effect for solving paramonotone variational inequalities. Under standard assumptions, we prove that the trajectories of this dynamical system converges to a solution of the variational inequality problem. A time discretization of this dynamical system provides an iterative inertial projection-type method. Our result generalizes and improves the existing results. Some numerical examples are given to confirm the theoretical results and illustrate the effectiveness of the proposed algorithms.