Finite-Value Superiorization for Variational Inequality Problems

TL;DR

This paper introduces a finite-value superiorization method for variational inequality problems, offering a simple iterative algorithm that computes approximate solutions efficiently by treating the problem as a perturbed convex feasibility task.

Contribution

It presents a novel finite-value superiorization approach tailored for variational inequalities, enabling efficient approximate solutions with controlled accuracy.

Findings

The algorithm effectively computes approximate solutions.

Finite-value perturbation improves computational efficiency.

The method guarantees prescribed accuracy in solutions.

Abstract

The main goal of this paper is to present the application of a superiorization methodology to solution of variational inequalities. Within this framework a variational inequality operator is considered as a small perturbation of a convex feasibility solver what allows to construct a simple iteration algorithm. The specific features of variational inequality problems allow to use a finite-value perturbation which may be advantageous from computational point of view. The price for simplicity and finite-value is that the algorithm provides an approximate solution of variational inequality problem with a prescribed coordinate accuracy.