@article{11c1f22312d14defa697f0671c09489e,
title = "A derivative-free three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration",
abstract = "In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing.",
keywords = "65K05, 65L09, 90C30, Unconstrained optimization, compressive sensing, conjugate gradient method, derivative-free method, nonlinear equations, projection method",
author = "{Hassan Ibrahim}, Abdulkarim and Poom Kumam and Hassan, {Basim A.} and {Bala Abubakar}, Auwal and Jamilu Abubakar",
note = "Funding Information: We are grateful to the anonymous referees for their useful comments, which have made the paper clearer and more comprehensive than the earlier version. The first author was supported by the {\textquoteleft}Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut's University of Technology Thonburi{\textquoteright} (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 research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The fourth author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. Funding Information: The first author was supported by the {\textquoteleft}Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut's University of Technology Thonburi{\textquoteright} (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 research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. We are grateful to the anonymous referees for their useful comments, which have made the paper clearer and more comprehensive than the earlier version. The first author was supported by the {\textquoteleft}Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut's University of Technology Thonburi{\textquoteright} (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 research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The fourth author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. Publisher Copyright: {\textcopyright} 2021 Informa UK Limited, trading as Taylor & Francis Group.",
year = "2022",
doi = "10.1080/00207160.2021.1946043",
language = "English",
volume = "99",
pages = "1041--1065",
journal = "International Journal of Computer Mathematics",
issn = "0020-7160",
publisher = "Taylor and Francis Ltd.",
number = "5",
}