论文标题
足够的下降riemannian结合梯度法
Sufficient Descent Riemannian Conjugate Gradient Method
论文作者
论文摘要
本文考虑了带有线路搜索算法的足够下降riemannian结合梯度方法。我们提出了两种足够的后裔非线性共轭梯度方法，并证明这些方法即使在Riemannian歧管上也满足了足够的下降状态。一种是将Fletcher-Reeves型方法与polak-ribiere-polyak-type方法相结合的混合方法，另一种是Hager-Zhang型方法，这两种方法都是在欧几里得空间中使用的概括。同样，我们概括了两种在欧几里得空间中广泛使用的线路搜索算法。此外，我们通过求解几个Riemannian优化问题来数字比较我们的广义方法。结果表明，所提出的混合方法的性能在很大程度上取决于所使用的线路搜索类型。同时，无论使用的线搜索类型如何，Hager-Zhang型方法具有快速收敛属性。
This paper considers sufficient descent Riemannian conjugate gradient methods with line search algorithms. We propose two kinds of sufficient descent nonlinear conjugate gradient methods and prove these methods satisfy the sufficient descent condition even on Riemannian manifolds. One is the hybrid method combining the Fletcher-Reeves-type method with the Polak-Ribiere-Polyak-type method, and the other is the Hager-Zhang-type method, both of which are generalizations of those used in Euclidean space. Also, we generalize two kinds of line search algorithms that are widely used in Euclidean space. In addition, we numerically compare our generalized methods by solving several Riemannian optimization problems. The results show that the performance of the proposed hybrid method greatly depends regardless of the type of line search used. Meanwhile, the Hager-Zhang-type method has the fast convergence property regardless of the type of line search used.
