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A derivative‐free scaling memoryless Broyden–Fletcher–Goldfarb–Shanno method for solving a system of monotone nonlinear equations

A derivative‐free scaling memoryless Broyden–Fletcher–Goldfarb–Shanno method for solving a system... This paper presents the two‐parameter scaling memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) method for solving a system of monotone nonlinear equations. The optimal values of the scaling parameters are obtained by minimizing the measure function involving all the eigenvalues of the memoryless BFGS matrix. The optimal values can be used in the analysis of the quasi‐Newton method for ill‐conditioned matrices. This algorithm can also be described as a combination of the projection technique and memoryless BGFS method. Global convergence of the method is provided. For validation and efficiency of the scheme, some test problems are computed and compared with existing results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerical Linear Algebra With Applications Wiley

A derivative‐free scaling memoryless Broyden–Fletcher–Goldfarb–Shanno method for solving a system of monotone nonlinear equations

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References (62)

Publisher
Wiley
Copyright
© 2021 John Wiley & Sons, Ltd.
ISSN
1070-5325
eISSN
1099-1506
DOI
10.1002/nla.2374
Publisher site
See Article on Publisher Site

Abstract

This paper presents the two‐parameter scaling memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) method for solving a system of monotone nonlinear equations. The optimal values of the scaling parameters are obtained by minimizing the measure function involving all the eigenvalues of the memoryless BFGS matrix. The optimal values can be used in the analysis of the quasi‐Newton method for ill‐conditioned matrices. This algorithm can also be described as a combination of the projection technique and memoryless BGFS method. Global convergence of the method is provided. For validation and efficiency of the scheme, some test problems are computed and compared with existing results.

Journal

Numerical Linear Algebra With ApplicationsWiley

Published: Oct 1, 2021

Keywords: global convergence

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