A generalized strong convergence algorithm in the presence of the errors for the variational inequality problems in Hilbert spaces

TL;DR

This paper introduces a generalized strong convergence algorithm for variational inequality problems in Hilbert spaces, capable of handling computational errors and demonstrating effectiveness through numerical examples.

Contribution

It extends previous algorithms by refining conditions and proving convergence despite computational errors, with practical validation via MATLAB simulations.

Findings

Algorithm converges strongly in the presence of errors

Numerical examples confirm effectiveness and robustness

Comparison shows improved performance over existing methods

Abstract

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's conditions and we have proved the convergence of the algorithm in the presence of some computational errors. Then using MATLAB software, the result will by illustrated in some numerical examples. Finally, we compare our algorithm with some other well known algorithms.