Quasi-Quadratic Gradient: A New Direction for Accelerating the BFGS Method in Quasi-Newton Optimization
Optimization and Control
2026-04-28 v1 Artificial Intelligence
Abstract
In this paper, we introduce the Quasi-Quadratic Gradient (QQG), a novel search direction designed to accelerate the BFGS method within the quasi-Newton framework. By defining the QQG as the product of the inverse Hessian approximation and the current gradient, we explicitly leverage local second-order curvature to rectify the search path. Theoretical analysis and empirical results demonstrate that our approach significantly outperforms vanilla BFGS in convergence speed while maintaining computational efficiency.
Cite
@article{arxiv.2604.23922,
title = {Quasi-Quadratic Gradient: A New Direction for Accelerating the BFGS Method in Quasi-Newton Optimization},
author = {John Chiang},
journal= {arXiv preprint arXiv:2604.23922},
year = {2026}
}