Watanjeet Singh | Searcharxiv

arXiv2026

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

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.

math.FA↗

arXiv2025

Convergence analysis for pseudo-monotone variational inequality problem involving projections onto a moving ball

This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set $\mathfrak{C}$ or onto a half-space containing $\mathfrak{C}$. However, computing projections onto a complicated feasible set can be difficult, and projections onto a half-space may fall outside $\mathfrak{C}$. Keeping this in mind, we aim to develop an iterative scheme that projects onto a ball that is contained in a feasible set and has an explicit expression. Our iterative scheme does not require prior knowledge of the Lipschitz constant of the cost operator. Finally, we provide some numerical experiments to show the effectiveness of our algorithm.

math.OC↗