# Quasi-Newton method of Optimization is proved to be a steepest descent method under the ellipsoid norm

arXiv: https://arxiv.org/abs/2411.11286 · HTML: https://mlsanity.com/paper/2411.11286/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2024.

## Built on by (most cited first, 1 of 1)

- [Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods](https://mlsanity.com/paper/2510.10777/) (2025)

## Abstract (arXiv)

Optimization problems, arise in many practical applications, from the view points of both theory and numerical methods. Especially, significant improvement in deep learning training came from the Quasi-Newton methods. Quasi-Newton search directions provide an attractive alternative to Newton's method in that they do not require computation of the Hessian and yet still attain a super linear rate of convergence. In Quasi-Newton method, we require Hessian approximation to satisfy the secant equation. In this paper, the Classical Cauchy-Schwartz Inequality is introduced, then more generalization are proposed. And it is seriously proved that Quasi-Newton method is a steepest descent method under the ellipsoid norm.