@article{3788ac4507934a2aa699459281f1914b,
title = "PRP-like algorithm for monotone operator equations",
abstract = "Many studies have been devoted to develop and improve the iterative methods for solving convex constraint nonlinear equations problem (CCP). Based on the projection technique, we introduce a derivative-free method for approximating the solution of CCP. The proposed method is suitable for solving large-scale nonlinear equations due to its lower storage requirements. The directions generated by the proposed method at every iteration are bounded. Under some mild conditions, we establish the global convergence result of the proposed method. Numerical experiments are provided to show the efficiency of the method in solving CCP. Moreover, we tested the capability of the method in solving the monotone nonlinear operator equation equivalent to the ℓ1-norm regularized minimization problem.",
keywords = "Conjugate gradient, Image restoration, Nonlinear equations, Projection method",
author = "Abubakar, {Auwal Bala} and Poom Kumam and Hassan Mohammad and Ibrahim, {Abdulkarim Hassan}",
note = "Funding Information: The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Also, the (first) author, (Dr. Auwal Bala Abubakar) would like to thank the Postdoctoral Fellowship from King Mongkut{\textquoteright}s University of Technology Thonburi (KMUTT), Thailand. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The first author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. Funding Information: The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Also, the (first) author, (Dr. Auwal Bala Abubakar) would like to thank the Postdoctoral Fellowship from King Mongkut{\textquoteright}s University of Technology Thonburi (KMUTT), Thailand. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The first author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. Publisher Copyright: {\textcopyright} 2021, The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature.",
year = "2021",
month = sep,
doi = "10.1007/s13160-021-00462-2",
language = "English",
volume = "38",
pages = "805--822",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
number = "3",
}