Riemannian Trust Region Methods for SC$^1$ Minimization
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911895717412864 |
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| author | Zhang, Chenyu Xiao, Rufeng Huang, Wen Jiang, Rujun |
| author_facet | Zhang, Chenyu Xiao, Rufeng Huang, Wen Jiang, Rujun |
| contents | Manifold optimization has recently gained significant attention due to its wide range of applications in various areas. This paper introduces the first Riemannian trust region method for minimizing an SC$^1$ function, which is a differentiable function that has a semismooth gradient vector field, on manifolds with convergence guarantee. We provide proof of both global and local convergence results, along with demonstrating the local superlinear convergence rate of our proposed method. As an application and to demonstrate our motivation, we utilize our trust region method as a subproblem solver within an augmented Lagrangian method for minimizing nonsmooth nonconvex functions over manifolds. This represents the first approach that fully explores the second-order information of the subproblem in the context of augmented Lagrangian methods on manifolds. Numerical experiments confirm that our method outperforms existing methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00490 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Riemannian Trust Region Methods for SC$^1$ Minimization Zhang, Chenyu Xiao, Rufeng Huang, Wen Jiang, Rujun Optimization and Control 90C30, 49J52, 65K05, 90C26 Manifold optimization has recently gained significant attention due to its wide range of applications in various areas. This paper introduces the first Riemannian trust region method for minimizing an SC$^1$ function, which is a differentiable function that has a semismooth gradient vector field, on manifolds with convergence guarantee. We provide proof of both global and local convergence results, along with demonstrating the local superlinear convergence rate of our proposed method. As an application and to demonstrate our motivation, we utilize our trust region method as a subproblem solver within an augmented Lagrangian method for minimizing nonsmooth nonconvex functions over manifolds. This represents the first approach that fully explores the second-order information of the subproblem in the context of augmented Lagrangian methods on manifolds. Numerical experiments confirm that our method outperforms existing methods. |
| title | Riemannian Trust Region Methods for SC$^1$ Minimization |
| topic | Optimization and Control 90C30, 49J52, 65K05, 90C26 |
| url | https://arxiv.org/abs/2307.00490 |