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

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

doi:10.1016/j.heliyon.2020.e05400

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

Heliyon. 2020 Nov 24;6(11):e05400. doi: 10.1016/j.heliyon.2020.e05400. eCollection 2020 Nov.

Authors

Auwal Bala Abubakar^{1

2

3}, Poom Kumam^{1

4}, Abdulkarim Hassan Ibrahim¹, Jewaidu Rilwan^{1

2}

Affiliations

¹ 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.
² Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Kano, Nigeria.
³ Numerical Optimization Research Group, Bayero University, Kano, Nigeria.
⁴ 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.

Abstract

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.

Keywords: Conjugate gradient; Image restoration; Mathematics; Nonlinear equations; Projection method.