A modified double inertial subgradient extragradient algorithm for non-monotone variational inequality with applications

TL;DR

This paper introduces a modified double inertial extragradient algorithm for non-monotone variational inequalities, featuring a self-adaptive step-size and projection technique, with proven convergence and demonstrated effectiveness through numerical experiments.

Contribution

It proposes a novel iterative method with adaptive step-size for non-monotone variational inequalities, including convergence analysis and practical numerical validation.

Findings

Weak convergence for non-monotone operators

Linear convergence under simplified conditions

Numerical experiments show improved performance

Abstract

This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized half-space and a self-adaptive step-size rule which works without prior knowledge of the Lipschitz constant of the operator. We establish a weak convergence result for a variational inequality involving a non-monotone cost operator along with weak and strong convergence results for quasi-monotone and strongly pseudo-monotone operators, respectively. Under a simplified framework, linear convergence of the proposed method is also discussed. Additionally, we provide some numerical experiments to demonstrate the effectiveness of our iterative algorithm compared to previously established algorithms in solving real-world applications. Finally, we carry out a sensitivity analysis of our algorithm to demonstrate its effectiveness across various parameter settings.