Inexact Newton Methods for Solving Generalized Equations on Riemannian Manifolds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914955405557760 |
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| author | Louzeiro, Mauricio S. Silva, Gilson N. Yuan, Jinyun Zhang, Daoping |
| author_facet | Louzeiro, Mauricio S. Silva, Gilson N. Yuan, Jinyun Zhang, Daoping |
| contents | The convergence of inexact Newton methods is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property, which is also explored. Under appropriate conditions and without any additional geometric assumptions, local convergence results with linear and quadratic rates, as well as a semi-local convergence result, are obtained for the proposed method. Finally, the theory is applied to the problem of finding a singularity for the sum of two vector fields. In particular, the KKT system for the constrained Riemannian center of mass on the sphere is explored numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10554 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inexact Newton Methods for Solving Generalized Equations on Riemannian Manifolds Louzeiro, Mauricio S. Silva, Gilson N. Yuan, Jinyun Zhang, Daoping Numerical Analysis Optimization and Control The convergence of inexact Newton methods is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property, which is also explored. Under appropriate conditions and without any additional geometric assumptions, local convergence results with linear and quadratic rates, as well as a semi-local convergence result, are obtained for the proposed method. Finally, the theory is applied to the problem of finding a singularity for the sum of two vector fields. In particular, the KKT system for the constrained Riemannian center of mass on the sphere is explored numerically. |
| title | Inexact Newton Methods for Solving Generalized Equations on Riemannian Manifolds |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2303.10554 |