This paper presents Riemannian conjugate gradient methods and global convergence analyses under the strong Wolfe conditions. The main idea of the proposed methods is to combine the good global convergence properties of the Dai–Yuan method with the efficient numerical performance of the Hestenes–Stiefel method. One of the proposed algorithms is a generalization to Riemannian manifolds of the hybrid conjugate gradient method of the Dai and Yuan in Euclidean space. The proposed methods are compared well numerically with the existing methods for solving several Riemannian optimization problems. Python implementations of the methods used in the numerical experiments are available at https://github.com/iiduka-researches/202008-hybrid-rcg.

本文介绍了强Wolfe条件下的黎曼共轭梯度法和全局收敛性分析。提出的方法的主要思想是将Dai-Yuan方法的良好全局收敛性与Hestenes-Stiefel方法的有效数值性能相结合。所提出的算法之一是对欧氏空间中the和元的混合共轭梯度法的黎曼流形的推广。将所提出的方法与现有方法进行了数值比较，从而解决了一些黎曼优化问题。可在https://github.com/iiduka-researches/202008-hybrid-rcg上获得用于数值实验的方法的Python实现。