# A Dai-Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions

arXiv: https://arxiv.org/abs/1405.4371 · HTML: https://mlsanity.com/paper/1405.4371/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2014.

## Built on by (most cited first, 3 of 3)

- [Riemannian Hamiltonian methods for min-max optimization on manifolds](https://mlsanity.com/paper/2204.11418/) (2022)
- [Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function](https://mlsanity.com/paper/2112.14949/) (2021)
- [Stiefel-AdamW: Geometry-Aware AdamW for Linear Factorization Blocks](https://mlsanity.com/paper/2609.21039/) (2026)

## Abstract (arXiv)

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.