Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates
Optimization and Control
2021-02-09 v2 Numerical Analysis
Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2011.03358,
title = {Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates},
author = {Damien Scieur and Lewis Liu and Thomas Pumir and Nicolas Boumal},
journal= {arXiv preprint arXiv:2011.03358},
year = {2021}
}
Comments
AISTATS 2021