@article{76f8a75a34124c81ab9e64d6c786c66f,
title = "Accelerated derivative-free method for nonlinear monotone equations with an application",
abstract = "In optimization theory, to speed up the convergence of iterative procedures, many mathematicians often use the inertial extrapolation method. In this article, based on the three-term derivative-free method for solving monotone nonlinear equations with convex constraints [Calcolo, 2016;53(2):133-145], we design an inertial algorithm for finding the solutions of nonlinear equation with monotone and Lipschitz continuous operator. The convergence analysis is established under some mild conditions. Furthermore, numerical experiments are implemented to illustrate the behavior of the new algorithm. The numerical results have shown the effectiveness and fast convergence of the proposed inertial algorithm over the existing algorithm. Moreover, as an application, we extend this method to solve the LASSO problem to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of the method.",
keywords = "derivative-free method, inertial algorithm, iterative method, nonlinear equations, projection method",
author = "{Hassan Ibrahim}, Abdulkarim and Poom Kumam and Auwal Bala Abubakar and Abubakar Adamu",
note = "Funding Information: We are grateful to the anonymous referees and associate editor for their useful comments, which have made the paper clearer and more comprehensive than the earlier version. The first author was supported by the Petchra Pra Jom Klao PhD Research Scholarship from King Mongkut's University of Technology Thonburi (Grant no. 16/2561). The authors also acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS‐CoE), KMUTT. Moreover, this project is funded by National Council of Thailand (NRCT) under Research Grants for Talented Mid‐Career Researchers (Contract no. N41A640089). The third author acknowledges with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. Funding Information: information Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT, King Mongkut's University of Technology Thonburi, National Council of Thailand (NRCT)We are grateful to the anonymous referees and associate editor for their useful comments, which have made the paper clearer and more comprehensive than the earlier version. The first author was supported by the Petchra Pra Jom Klao PhD Research Scholarship from King Mongkut's University of Technology Thonburi (Grant no. 16/2561). The authors also acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this project is funded by National Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract no. N41A640089). The third author acknowledges with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. Publisher Copyright: {\textcopyright} 2021 John Wiley & Sons Ltd.",
year = "2022",
month = may,
doi = "10.1002/nla.2424",
language = "English",
volume = "29",
journal = "Numerical Linear Algebra with Applications",
issn = "1070-5325",
publisher = "John Wiley and Sons Ltd",
number = "3",
}