TY - JOUR
T1 - On the derivative-free quasi-Newton-type algorithm for separable systems of nonlinear equations
AU - Mohammad, Hassan
AU - Muhammed Awwal, Aliyu
AU - Bala Abubakar, Auwal
AU - Salihu Ben Musa, Ahmad
N1 - Publisher Copyright:
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021.
PY - 2021/11/1
Y1 - 2021/11/1
N2 - 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.
AB - 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.
KW - Convergence
KW - Derivative-free methods
KW - Numerical experiments
KW - Quasi-Newton-type methods
KW - Separable nonlinear equations
UR - http://www.scopus.com/inward/record.url?scp=85119413854&partnerID=8YFLogxK
U2 - 10.1051/ro/2021154
DO - 10.1051/ro/2021154
M3 - Article
AN - SCOPUS:85119413854
SN - 0399-0559
VL - 55
SP - 3293
EP - 3316
JO - RAIRO - Operations Research
JF - RAIRO - Operations Research
IS - 6
ER -