Inertial extragradient algorithms for solving variational inequalities and fixed point problems

TL;DR

This paper introduces four inertial extragradient algorithms to solve convex feasibility problems involving variational inequalities and fixed point problems, demonstrating their convergence and efficiency through theoretical analysis and computational tests.

Contribution

The paper proposes novel inertial extragradient algorithms with simple step sizes for combined variational inequality and fixed point problems, establishing their strong convergence.

Findings

Algorithms converge strongly under standard conditions.

Computational tests show improved efficiency over existing methods.

Proposed methods effectively solve combined variational inequality and fixed point problems.

Abstract

The objective of this research is to explore a convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem. We introduce four inertial extragradient algorithms that are motivated by the inertial method, the subgradient extragradient method, the Tseng's extragradient method and the Mann-type method endowed with a simple step size. Strong convergence theorems of the algorithms are established under some standard and suitable conditions enforced by the cost operators. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.