  This article describes a new Riemannian conjugate gradient method and
presents a global convergence analysis. The existing Fletcher-Reeves-type
Riemannian conjugate gradient method is guaranteed to be globally convergent if
it is implemented with the strong Wolfe conditions. On the other hand, the
Dai-Yuan-type Euclidean conjugate gradient method generates globally convergent
sequences under the weak Wolfe conditions. This article deals with a
generalization of Dai-Yuan's Euclidean algorithm to a Riemannian algorithm that
requires only the weak Wolfe conditions. The global convergence property of the
proposed method is proved by means of the scaled vector transport associated
with the differentiated retraction. The results of numerical experiments
demonstrate the effectiveness of the proposed algorithm.
