Proximal and Contraction method with Relaxed Inertial and Correction Terms for Solving Mixed Variational Inequality Problems

TL;DR

This paper introduces an advanced proximal and contraction method with inertial, correction, and relaxation techniques to efficiently solve convex mixed variational inequality problems, demonstrating improved convergence and practical effectiveness.

Contribution

It presents a novel combination of inertial, correction, and relaxation strategies within a proximal and contraction framework for variational inequalities.

Findings

Weak convergence under mild assumptions

Numerical results show improved convergence

Effectiveness of relaxation and inertial terms

Abstract

We propose in this paper a proximal and contraction method for solving a convex mixed variational inequality problem in a real Hilbert space. To accelerate the convergence of our proposed method, we incorporate an inertial extrapolation term, two correction terms, and a relaxation technique. We therefore obtain a weak convergence result under some mild assumptions. Finally, we present numerical examples to practically demonstrate the effectiveness of the relaxation technique, the inertial extrapolation term, and the correction terms in our proposed method.