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 -