Quasi-Quadratic Gradient: A New Direction for Accelerating the BFGS Method in Quasi-Newton Optimization

John Chiang

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arXiv · 2604.23922

Quasi-Quadratic Gradient: A New Direction for Accelerating the BFGS Method in Quasi-Newton Optimization

John Chiang

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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.

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BibTeX RIS

John Chiang. 2026-04-27. Quasi-Quadratic Gradient: A New Direction for Accelerating the BFGS Method in Quasi-Newton Optimization. https://arxiv.org/abs/2604.23922

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