Convergence of a quasi-Newton method for solving systems of nonlinear underdetermined equations

N. Vater () and A. Borzì ()
Additional contact information
N. Vater: Universität Würzburg
A. Borzì: Universität Würzburg

Computational Optimization and Applications, 2025, vol. 91, issue 2, No 20, 973-996

Abstract: Abstract The development and convergence analysis of a quasi-Newton method for the solution of systems of nonlinear underdetermined equations is investigated. These equations arise in many application fields, e.g., supervised learning of large overparameterised neural networks, which require the development of efficient methods with guaranteed convergence. In this paper, a new approach for the computation of the Moore–Penrose inverse of the approximate Jacobian coming from the Broyden update is presented and a semi-local convergence result for a damped quasi-Newton method is proved. The theoretical results are illustrated in detail for the case of systems of multidimensional quadratic equations, and validated in the context of eigenvalue problems and supervised learning of overparameterised neural networks.

Keywords: Systems of nonlinear underdetermined equations; Nonlinear root-finding problems; Quasi-Newton methods; Least change secant update; Supervised learning; 49M15; 65H04; 65H10; 90C30 (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-024-00606-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:91:y:2025:i:2:d:10.1007_s10589-024-00606-3

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-024-00606-3

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().