Tseng's Type Methods in Continuous and Discrete Time for Quasi-Variational Inequalities

TL;DR

This paper extends Tseng's scheme to approximate solutions for quasi-variational inequalities in Hilbert spaces, analyzing convergence, equilibrium existence, and linear convergence in discretized systems.

Contribution

It introduces a modified Tseng's scheme for quasi-variational inequalities and studies convergence and equilibrium properties in both continuous and discrete settings.

Findings

Existence of equilibrium points established.

Convergence results for the modified scheme demonstrated.

Linear convergence in discretized systems shown through examples.

Abstract

This paper presents an approach for obtaining approximate solutions to quasi-variational inequalities in a real Hilbert space by modifying Tseng's scheme, which was originally designed for variational inequalities. The study explores the existence of equilibrium points and investigates convergence results related to dynamical systems. Linear convergence for discretized systems is examined through examples, illustrations, and special cases.