Center of Excellence in Theoretical and Computational Science (TaCS-CoE) and KMUTTFixed Point, Research Laboratory, Room SCL 802 Fixed Point Laboratory Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Thung Khru, Bangkok, Thailand.
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University Zaria, Kaduna, Nigeria.
PLoS One. 2024 May 15;19(5):e0302441. doi: 10.1371/journal.pone.0302441. eCollection 2024.
Several conjugate gradient (CG) parameters resulted in promising methods for optimization problems. However, it turns out that some of these parameters, for example, 'PRP,' 'HS,' and 'DL,' do not guarantee sufficient descent of the search direction. In this work, we introduce new spectral-like CG methods that achieve sufficient descent property independently of any line search (LSE) and for arbitrary nonnegative CG parameters. We establish the global convergence of these methods for four different parameters using Wolfe LSE. Our algorithm achieves this without regular restart and assumption of convexity regarding the objective functions. The sequences generated by our algorithm identify points that satisfy the first-order necessary condition for Pareto optimality. We conduct computational experiments to showcase the implementation and effectiveness of the proposed methods. The proposed spectral-like methods, namely nonnegative SPRP, SHZ, SDL, and SHS, exhibit superior performance based on their arrangement, outperforming HZ and SP methods in terms of the number of iterations, function evaluations, and gradient evaluations.
几种共轭梯度 (CG) 参数在优化问题中产生了有前途的方法。然而，事实证明，其中一些参数，例如 'PRP'、'HS' 和 'DL'，并不能保证搜索方向有足够的下降。在这项工作中，我们引入了新的谱类 CG 方法，这些方法在不依赖任何线搜索 (LSE) 和任意非负 CG 参数的情况下实现了充分下降特性。我们使用 Wolfe LSE 为这四种不同的参数建立了这些方法的全局收敛性。我们的算法在不进行常规重启和目标函数凸性假设的情况下实现了这一点。我们的算法生成的序列确定了满足帕累托最优的一阶必要条件的点。我们进行了计算实验，展示了所提出方法的实现和有效性。所提出的谱类方法，即非负 SPRP、SHZ、SDL 和 SHS，根据它们的排列表现出优越的性能，在迭代次数、函数评估和梯度评估方面优于 HZ 和 SP 方法。
