On diagonally structured scheme for nonlinear least squares and data-fitting problems
Journal article
Authors/Editors
Strategic Research Themes
Publication Details
Author list: Yahaya M.M.; Kumam P.; Chaipunya P.; Awwal A.M.; Wang L.
Publisher: EDP Sciences
Publication year: 2024
Volume number: 58
Issue number: 4
Start page: 2887
End page: 2905
Number of pages: 19
ISSN: 0399-0559
eISSN: 1290-3868
Languages: English-Great Britain (EN-GB)
Abstract
Recently, structured nonlinear least-squares (NLS) based algorithms gained considerable emphasis from researchers; this attention may result from increasingly applicable areas of these algorithms in different science and engineering domains. In this article, we coined a new efficient structured-based NLS algorithm. We developed a diagonal Hessian-based formulation for solving NLS problems. We derived the quasi-Newton update based on a diagonal matrix scheme subject to a modified structured secant condition. Also, we show that the algorithm's search direction satisfies a sufficient descent condition under some standard assumptions. Subsequently, we also prove the global convergence of the algorithm and then eventually show its linear convergence rate for strongly convex functions. Furthermore, to show case the proposed algorithm's performance, we experimented numerically by comparing it with other approaches on some benchmark test functions available in the literature. Finally, the introduced scheme is applied to solve some data-fitting problems © The authors. Published by EDP Sciences, ROADEF, SMAI 2024.
Keywords
Convergence rate, Data fitting, Diagonal update, Secant condition
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