Parallel projection methods for variational inequalities involving common fixed point problems

TL;DR

This paper introduces two new parallel projection algorithms to solve systems of variational inequalities that also involve common fixed points of pseudocontractive mappings, with practical numerical experiments demonstrating efficiency.

Contribution

The paper presents novel parallel projection methods for variational inequalities involving common fixed points, including a technical extension for large-scale problems.

Findings

Algorithms effectively solve large systems of variational inequalities.

Numerical experiments confirm the efficiency of parallel computations.

Proposed methods outperform traditional approaches in computational speed.

Abstract

In this paper, we introduce two novel parallel projection methods for finding a solution of a system of variational inequalities which is also a common fixed point of a family of (asymptotically) $\kappa$ - strict pseudocontractive mappings. A technical extension in the proposed algorithms helps in computing practical numerical experiments when the number of subproblems is large. Some numerical examples are implemented to demonstrate the efficiency of parallel computations.