Issue |
RAIRO-Oper. Res.
Volume 55, Number 6, November-December 2021
|
|
---|---|---|
Page(s) | 3293 - 3316 | |
DOI | https://doi.org/10.1051/ro/2021154 | |
Published online | 15 November 2021 |
On the derivative-free quasi-Newton-type algorithm for separable systems of nonlinear equations
1
Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Nigeria
2
Numerical Optimization Research Group, Bayero University, Kano, Nigeria
3
Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria
4
KMUTT Fixed 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, Thrung Khru, Bangkok, 10140, Thailand
5
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa 0204, South Africa
6
Department of Computer Science, Federal College of Agricultural Produce Technology, Kano, Nigeria
* Corresponding author: hmuhd.mth@buk.edu.ng
Received:
27
December
2020
Accepted:
9
October
2021
A derivative-free quasi-Newton-type algorithm in which its search direction is a product of a positive definite diagonal matrix and a residual vector is presented. The algorithm is simple to implement and has the ability to solve large-scale nonlinear systems of equations with separable functions. The diagonal matrix is simply obtained in a quasi-Newton manner at each iteration. Under some suitable conditions, the global and R-linear convergence result of the algorithm are presented. Numerical test on some benchmark separable nonlinear equations problems reveal the robustness and efficiency of the algorithm.
Mathematics Subject Classification: 65K05 / 65H10 / 90C30 / 90C53
Key words: Separable nonlinear equations / derivative-free methods / quasi-Newton-type methods / convergence / numerical experiments
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.