Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/323336 
Year of Publication: 
2024
Citation: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 91 [Issue:] 2 [Publisher:] Springer US [Place:] New York [Year:] 2024 [Pages:] 973-996
Publisher: 
Springer US, New York
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.
Subjects: 
Systems of nonlinear underdetermined equations
Nonlinear root-finding problems
Quasi-Newton methods
Least change secant update
Supervised learning
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version
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