Center of Excellence in Theoretical and Computational Science, Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok, Thailand.
Department of Mathematics, Faculty of Sciences, Modibbo Adama University, Yola, Nigeria.
PLoS One. 2023 Mar 16;18(3):e0281250. doi: 10.1371/journal.pone.0281250. eCollection 2023.
In 2012, Rivaie et al. introduced RMIL conjugate gradient (CG) method which is globally convergent under the exact line search. Later, Dai (2016) pointed out abnormality in the convergence result and thus, imposed certain restricted RMIL CG parameter as a remedy. In this paper, we suggest an efficient RMIL spectral CG method. The remarkable feature of this method is that, the convergence result is free from additional condition usually imposed on RMIL. Subsequently, the search direction is sufficiently descent independent of any line search technique. Thus, numerical experiments on some set of benchmark problems indicate that the method is promising and efficient. Furthermore, the efficiency of the proposed method is demonstrated on applications arising from arm robotic model and image restoration problems.
2012 年，Rivaie 等人引入了 RMIL 共轭梯度（CG）方法，该方法在精确线搜索下具有全局收敛性。后来，戴（2016）指出收敛结果存在异常，因此施加了一定的限制 RMIL CG 参数作为补救措施。在本文中，我们提出了一种有效的 RMIL 谱 CG 方法。该方法的显著特点是，收敛结果不受通常施加在 RMIL 上的附加条件的限制。随后，搜索方向与任何线搜索技术无关，具有足够的下降性。因此，对一些基准问题集的数值实验表明，该方法是有前途和有效的。此外，还将该方法应用于手臂机器人模型和图像恢复问题。
