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

Jiongcheng Li

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arXiv · 2411.11286

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

Jiongcheng Li

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Abstract

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.

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Jiongcheng Li. 2024-11-18. Quasi-Newton method of Optimization is proved to be a steepest descent method under the ellipsoid norm. https://arxiv.org/abs/2411.11286

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