Proximal Quasi-Newton Method for Composite Optimization over the Stiefel Manifold
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913653431730176 |
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| author | Wang, Qinsi Yang, Wei Hong |
| author_facet | Wang, Qinsi Yang, Wei Hong |
| contents | In this paper, we consider the composite optimization problems over the Stiefel manifold. A successful method to solve this class of problems is the proximal gradient method proposed by Chen et al. Motivated by the proximal Newton-type techniques in the Euclidean space, we present a Riemannian proximal quasi-Newton method, named ManPQN, to solve the composite optimization problems. The global convergence of the ManPQN method is proved and iteration complexity for obtaining an $ε$-stationary point is analyzed. Under some mild conditions, we also establish the local linear convergence result of the ManPQN method. Numerical results are encouraging, which shows that the proximal quasi-Newton technique can be used to accelerate the proximal gradient method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proximal Quasi-Newton Method for Composite Optimization over the Stiefel Manifold Wang, Qinsi Yang, Wei Hong Optimization and Control 90C53 In this paper, we consider the composite optimization problems over the Stiefel manifold. A successful method to solve this class of problems is the proximal gradient method proposed by Chen et al. Motivated by the proximal Newton-type techniques in the Euclidean space, we present a Riemannian proximal quasi-Newton method, named ManPQN, to solve the composite optimization problems. The global convergence of the ManPQN method is proved and iteration complexity for obtaining an $ε$-stationary point is analyzed. Under some mild conditions, we also establish the local linear convergence result of the ManPQN method. Numerical results are encouraging, which shows that the proximal quasi-Newton technique can be used to accelerate the proximal gradient method. |
| title | Proximal Quasi-Newton Method for Composite Optimization over the Stiefel Manifold |
| topic | Optimization and Control 90C53 |
| url | https://arxiv.org/abs/2501.09516 |