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A Riemannian derivative-free Polak–Ribiére–Polyak method for tangent vector field
- Source :
- Numerical Algorithms. 86:325-355
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- 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–Ribiere–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.
- Subjects :
- Line search
Applied Mathematics
Numerical analysis
Field (mathematics)
010103 numerical & computational mathematics
Riemannian manifold
01 natural sciences
010101 applied mathematics
symbols.namesake
Theory of computation
Convergence (routing)
symbols
Applied mathematics
Mathematics::Differential Geometry
Tangent vector
0101 mathematics
Newton's method
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 86
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi...........f8a283a6b45a0cb8e1140344bdf8039e