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.
Keywords: Separable nonlinear equations, derivative-free methods, quasi-Newton-type methods, convergence, numerical experiments
@article{RO_2021__55_6_3293_0,
author = {Mohammad, Hassan and Muhammed Awwal, Aliyu and Bala Abubakar, Auwal and Salihu Ben Musa, Ahmad},
title = {On the derivative-free {quasi-Newton-type} algorithm for separable systems of nonlinear equations},
journal = {RAIRO. Operations Research},
pages = {3293--3316},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {6},
doi = {10.1051/ro/2021154},
mrnumber = {4338793},
zbl = {1483.65079},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021154/}
}
TY - JOUR AU - Mohammad, Hassan AU - Muhammed Awwal, Aliyu AU - Bala Abubakar, Auwal AU - Salihu Ben Musa, Ahmad TI - On the derivative-free quasi-Newton-type algorithm for separable systems of nonlinear equations JO - RAIRO. Operations Research PY - 2021 SP - 3293 EP - 3316 VL - 55 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021154/ DO - 10.1051/ro/2021154 LA - en ID - RO_2021__55_6_3293_0 ER -
%0 Journal Article %A Mohammad, Hassan %A Muhammed Awwal, Aliyu %A Bala Abubakar, Auwal %A Salihu Ben Musa, Ahmad %T On the derivative-free quasi-Newton-type algorithm for separable systems of nonlinear equations %J RAIRO. Operations Research %D 2021 %P 3293-3316 %V 55 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021154/ %R 10.1051/ro/2021154 %G en %F RO_2021__55_6_3293_0
Mohammad, Hassan; Muhammed Awwal, Aliyu; Bala Abubakar, Auwal; Salihu Ben Musa, Ahmad. On the derivative-free quasi-Newton-type algorithm for separable systems of nonlinear equations. RAIRO. Operations Research, Tome 55 (2021) no. 6, pp. 3293-3316. doi: 10.1051/ro/2021154
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