Computational Analysis of Variational Inequalities Using Mean Extra-Gradient Approach

An improved variational inequality strategy for dealing with variational inequality in a Hilbert space is proposed in this article as an alternative; if Hilbert space is used as the domain of interest, the original extra-gradient method is proposed for resolving variational inequality. This improved variational inequality strategy can be used as a substitute for the original extra-gradient method in some situations. Mann's mean value method, coupled with the widely used sub-gradient extra-gradient strategy, makes it possible to update all of the previous iterations in a single step, thus saving time and effort. All of this is made feasible via the use of Mann's mean value technique in conjunction with the convex hull of all prior iterations of the algorithm. It is guaranteed that the mean value iteration will result in an acceptable resolution of a variational inequality issue as long as one or more of the criteria for the averaging matrix are fulfilled. Numerous experiments were performed in order to demonstrate the correctness of the theoretical conclusion obtained.

Automated summary

This article proposes an improved variational inequality strategy for dealing with variational inequality in a Hilbert space. By combining Mann's mean value method with the widely used sub-gradient extra-gradient strategy, the previous iterations can be updated in a single step, saving time and effort. Experimental results demonstrate the correctness of the theoretical conclusion.