Abubakar Auwal Bala, Kumam Poom, Ibrahim Abdulkarim Hassan, Rilwan Jewaidu
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.
Heliyon. 2020 Nov 24;6(11):e05400. doi: 10.1016/j.heliyon.2020.e05400. eCollection 2020 Nov.
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.
提出了一种用于求解非线性方程和图像恢复的无导数共轭梯度算法。该算法的共轭梯度（CG）参数是Hestenes-Stiefel（HS）型和戴袁（DY）型CG参数的凸组合。搜索方向是下降且有界的。在适当的假设下，得到了所提混合算法的收敛性。通过一些基准测试问题，表明所提算法与现有算法相比是有效的。此外，所提算法被有效地应用于求解图像恢复问题。
