A Riemannian Derivative-Free Polak-Ribiere-Polyak Method for Tangent Vector Field
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866913619365593088 |
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| author | Yao, Teng-Teng Zhao, Zhi Bai, Zheng-Jian Jin, Xiao-Qing |
| author_facet | Yao, Teng-Teng Zhao, Zhi Bai, Zheng-Jian Jin, Xiao-Qing |
| contents | This paper is concerned with the problem of finding a zero of a tangent vector field on a Riemannian manifold. We first reformulate the problem as an equivalent Riemannian optimization problem. Then we propose a Riemannian derivative-free Polak-Ribiére-Polyak method for solving the Riemannian optimization problem, where a non-monotone line search is employed. The global convergence of the proposed method is established under some mild assumptions. To further improve the efficiency, we also provide a hybrid method, which combines the proposed geometric method with the Riemannian Newton method. Finally, some numerical experiments are reported to illustrate the efficiency of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_04700 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Riemannian Derivative-Free Polak-Ribiere-Polyak Method for Tangent Vector Field Yao, Teng-Teng Zhao, Zhi Bai, Zheng-Jian Jin, Xiao-Qing Numerical Analysis This paper is concerned with the problem of finding a zero of a tangent vector field on a Riemannian manifold. We first reformulate the problem as an equivalent Riemannian optimization problem. Then we propose a Riemannian derivative-free Polak-Ribiére-Polyak method for solving the Riemannian optimization problem, where a non-monotone line search is employed. The global convergence of the proposed method is established under some mild assumptions. To further improve the efficiency, we also provide a hybrid method, which combines the proposed geometric method with the Riemannian Newton method. Finally, some numerical experiments are reported to illustrate the efficiency of the proposed method. |
| title | A Riemannian Derivative-Free Polak-Ribiere-Polyak Method for Tangent Vector Field |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1901.04700 |