Global convergence of Hager--Zhang type Riemannian conjugate gradient method
Global convergence of Hager--Zhang type Riemannian conjugate gradient method
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Hager的全局收敛--张型黎曼共轭梯度法
DOI：
10.1016/j.amc.2022.127685
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发表时间：
2023
影响因子：
4
通讯作者：
Iiduka Hideaki
中科院分区：
文献类型：
--
作者：
Sakai Hiroyuki;Sato Hiroyuki;Iiduka Hideaki
本文提出了一种Hager-Zhang（HZ）型黎曼共轭梯度法。在两种假设条件下，我们也给出了我们所提出的方法的全局收敛性分析。此外，我们数值比较我们提出的方法与现有的方法，通过解决两种类型的黎曼优化问题的单位球。数值结果表明，我们提出的方法具有更好的性能比现有的方法，即，FR、DY、PRP和HS方法。特别是，他们表明，它有更高的性能比现有的方法，包括混合的计算图的稳定数的问题。
This paper presents the Hager–Zhang (HZ)-type Riemannian conjugate gradient method that uses the exponential retraction. We also present global convergence analyses of our proposed method under two kinds of assumptions. Moreover, we numerically compare our proposed methods with the existing methods by solving two kinds of Riemannian optimization problems on the unit sphere. The numerical results show that our proposed method has much better performance than the existing methods, i.e., the FR, DY, PRP, and HS methods. In particular, they show that it has much higher performance than existing methods including the hybrid ones in computing the stability number of graphs problem.