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On diagonally structured scheme for nonlinear least squares and data-fitting problems

Authors :
Yahaya, Mahmoud Muhammad
Kumam, Poom
Chaipunya, Parin
Awwal, Aliyu Muhammed
Wang, Lin
Yahaya, Mahmoud Muhammad
Kumam, Poom
Chaipunya, Parin
Awwal, Aliyu Muhammed
Wang, Lin
Source :
RAIRO - Operations Research; July 2024, Vol. 58 Issue: 4 p2887-2905, 19p
Publication Year :
2024

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

Details

Language :
English
ISSN :
03990559 and 12903868
Volume :
58
Issue :
4
Database :
Supplemental Index
Journal :
RAIRO - Operations Research
Publication Type :
Periodical
Accession number :
ejs67038906
Full Text :
https://doi.org/10.1051/ro/2024102