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

2025/11/23 by Nwakpa, Chidi Elijah, Ofem, Austine Efut, Okorie, Kalu Okam +2
Computer Science · Mathematics · #47H09 #47H10 #49J53 #90C25 #Advanced Optimization Algorithms Research #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · doi:10.48550/arxiv.2511.18652

openalex publication_date 2025/11/23 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

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.

Citations

• Minimax theorems in a fully non-convex setting
• Performance of first-order methods for smooth convex minimization: a novel approach

Related

• A general inertial proximal point method for mixed variational inequality problem
• A Third Order Dynamical System for Mixed Variational Inequalities
• Forward-Backward-Forward Dynamical System for Solving Mixed Variational Inequality Problems
• Proximal extrapolated gradient methods with prediction and correction for monotone variational inequalities
• Projection and contraction methods with double inertial steps for variational inclusion problems on Hilbert spaces