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

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Abstract

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.

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Acknowledgments

The author would like to thank the anonymous referees for their valuable comments that helped improve the paper significantly. This work was supported by JSPS (Japan Society for the Promotion of Science) KAKENHI Grant Number 26887037.

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  1. Department of Management Science, Tokyo University of Science, Tokyo, 162-8601, Japan

    Hiroyuki Sato

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  1. Hiroyuki Sato
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Correspondence to Hiroyuki Sato.

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Sato, H. A Dai–Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions. Comput Optim Appl 64, 101–118 (2016). https://doi.org/10.1007/s10589-015-9801-1

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  • DOI: https://doi.org/10.1007/s10589-015-9801-1

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