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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.

Keywords

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

R2 v1 2026-06-23T19:57:44.581Z