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
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.
