# Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates

arXiv: https://arxiv.org/abs/2011.03358 · HTML: https://mlsanity.com/paper/2011.03358/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [A Mini-Block Fisher Method for Deep Neural Networks](https://mlsanity.com/paper/2202.04124/) (2022)
- [Nys-Newton: Nystr"om-Approximated Curvature for Stochastic Optimization](https://mlsanity.com/paper/2110.08577/) (2021)
- [An Efficient Nonlinear Acceleration method that Exploits Symmetry of the Hessian](https://mlsanity.com/paper/2210.12573/) (2022)

## Abstract (arXiv)

Quasi-Newton techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other quasi-Newton schemes, such as BFGS, enforce symmetry but cannot satisfy more than one secant equation. We propose a new type of quasi-Newton symmetric update using several secant equations in a least-squares sense. Our approach generalizes and unifies the design of quasi-Newton updates and satisfies provable robustness guarantees.