Derivative-free HS-DY-type method for solving nonlinear equations and image restoration

A derivative-free conjugate gradient algorithm for solving nonlinear equations and image restoration is proposed. The conjugate gradient (CG) parameter of the proposed algorithm is a convex combination of Hestenes-Stiefel (HS) and Dai-Yuan (DY) type CG parameters. The search direction is descent and...

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Autores principales: Abubakar, Auwal Bala, Kumam, Poom, Ibrahim, Abdulkarim Hassan, Rilwan, Jewaidu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2020
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7695968/
https://www.ncbi.nlm.nih.gov/pubmed/33294653
http://dx.doi.org/10.1016/j.heliyon.2020.e05400
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author Abubakar, Auwal Bala
Kumam, Poom
Ibrahim, Abdulkarim Hassan
Rilwan, Jewaidu
author_facet Abubakar, Auwal Bala
Kumam, Poom
Ibrahim, Abdulkarim Hassan
Rilwan, Jewaidu
author_sort Abubakar, Auwal Bala
collection PubMed
description A derivative-free conjugate gradient algorithm for solving nonlinear equations and image restoration is proposed. The conjugate gradient (CG) parameter of the proposed algorithm is a convex combination of Hestenes-Stiefel (HS) and Dai-Yuan (DY) type CG parameters. The search direction is descent and bounded. Under suitable assumptions, the convergence of the proposed hybrid algorithm is obtained. Using some benchmark test problems, the proposed algorithm is shown to be efficient compared with existing algorithms. In addition, the proposed algorithm is effectively applied to solve image restoration problems.
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spelling pubmed-76959682020-12-07 Derivative-free HS-DY-type method for solving nonlinear equations and image restoration Abubakar, Auwal Bala Kumam, Poom Ibrahim, Abdulkarim Hassan Rilwan, Jewaidu Heliyon Research Article A derivative-free conjugate gradient algorithm for solving nonlinear equations and image restoration is proposed. The conjugate gradient (CG) parameter of the proposed algorithm is a convex combination of Hestenes-Stiefel (HS) and Dai-Yuan (DY) type CG parameters. The search direction is descent and bounded. Under suitable assumptions, the convergence of the proposed hybrid algorithm is obtained. Using some benchmark test problems, the proposed algorithm is shown to be efficient compared with existing algorithms. In addition, the proposed algorithm is effectively applied to solve image restoration problems. Elsevier 2020-11-24 /pmc/articles/PMC7695968/ /pubmed/33294653 http://dx.doi.org/10.1016/j.heliyon.2020.e05400 Text en © 2020 The Authors http://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
spellingShingle Research Article
Abubakar, Auwal Bala
Kumam, Poom
Ibrahim, Abdulkarim Hassan
Rilwan, Jewaidu
Derivative-free HS-DY-type method for solving nonlinear equations and image restoration
title Derivative-free HS-DY-type method for solving nonlinear equations and image restoration
title_full Derivative-free HS-DY-type method for solving nonlinear equations and image restoration
title_fullStr Derivative-free HS-DY-type method for solving nonlinear equations and image restoration
title_full_unstemmed Derivative-free HS-DY-type method for solving nonlinear equations and image restoration
title_short Derivative-free HS-DY-type method for solving nonlinear equations and image restoration
title_sort derivative-free hs-dy-type method for solving nonlinear equations and image restoration
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7695968/
https://www.ncbi.nlm.nih.gov/pubmed/33294653
http://dx.doi.org/10.1016/j.heliyon.2020.e05400
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AT ibrahimabdulkarimhassan derivativefreehsdytypemethodforsolvingnonlinearequationsandimagerestoration
AT rilwanjewaidu derivativefreehsdytypemethodforsolvingnonlinearequationsandimagerestoration

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