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A derivative‐free scaling memoryless Broyden–Fletcher–Goldfarb–Shanno method for solving a system of monotone nonlinear equations
Author(s) -
Ullah Najib,
Sabi'u Jamilu,
Shah Abdullah
Publication year - 2021
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2374
Subject(s) - broyden–fletcher–goldfarb–shanno algorithm , mathematics , monotone polygon , convergence (economics) , nonlinear system , eigenvalues and eigenvectors , scaling , quasi newton method , matrix (chemical analysis) , projection (relational algebra) , mathematical optimization , function (biology) , newton's method , algorithm , computer science , computer network , physics , geometry , asynchronous communication , materials science , quantum mechanics , evolutionary biology , economics , composite material , biology , economic growth
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.