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

Auwal Bala Abubakar; Poom Kumam; Abdulkarim Hassan Ibrahim; Jewaidu Rilwan

Heliyon (Nov 2020)

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

Auwal Bala Abubakar,
Poom Kumam,
Abdulkarim Hassan Ibrahim,
Jewaidu Rilwan

Affiliations

Auwal Bala Abubakar: Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand; Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Kano, Nigeria; Numerical Optimization Research Group, Bayero University, Kano, Nigeria
Poom Kumam: Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand; KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand; Corresponding author at: Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
Abdulkarim Hassan Ibrahim: Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
Jewaidu Rilwan: Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand; Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Kano, Nigeria

Journal volume & issue: Vol. 6, no. 11
p. e05400

Abstract

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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.

Published in Heliyon

ISSN: 2405-8440 (Online)
Publisher: Elsevier
Country of publisher: United Kingdom
LCC subjects: Science: Science (General); Social Sciences: Social sciences (General)
Website: https://www.cell.com/heliyon/home

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