Issue |
RAIRO-Oper. Res.
Volume 58, Number 4, July-August 2024
|
|
---|---|---|
Page(s) | 2887 - 2905 | |
DOI | https://doi.org/10.1051/ro/2024102 | |
Published online | 31 July 2024 |
On diagonally structured scheme for nonlinear least squares and data-fitting problems
1
Center of Excellence in Theoretical and Computational Science (TaCS-CoE) and KMUTTFixed Point, Research Laboratory, Room SCL 802 Fixed Point Laboratory Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
2
NCAO Research Center, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCSCoE), Faculty of Science, King Mongkut’s University of Technology, Thonburi (KMUTT), 126 Pracha-Uthit Rd, Bang Mod, Thung Khru, Bangkok 10140, Thailand
3
Department of Mathematics, Faculty of Science, Gombe State University, Gombe 760214, Nigeria
4
Office of Science and Research, Yunnan University of Finance and Economics, Kunming, P.R. China
* Corresponding author: poom.kum@kmutt.ac.th
Received:
1
October
2022
Accepted:
6
May
2024
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
Mathematics Subject Classification: 93E24 / 90C53 / 65D10
Key words: Data fitting / diagonal update / nonlinear least squares / secant condition / convergence rate
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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