A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909893749899264 |
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| author | Zheng, Zhong Yu, Xin Ma, Shiqian Xue, Lingzhou |
| author_facet | Zheng, Zhong Yu, Xin Ma, Shiqian Xue, Lingzhou |
| contents | This paper proposes a new inexact manifold proximal linear (IManPL) algorithm for solving nonsmooth, nonconvex composite optimization problems over an embedded submanifold. At each iteration, IManPL solves a convex subproblem inexactly, guided by two adaptive stopping criteria. We establish convergence guarantees and show that IManPL achieves the best first-order oracle complexity for solving this class of problems. Numerical experiments on sparse spectral clustering and sparse principal component analysis demonstrate that our methods outperform existing approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria Zheng, Zhong Yu, Xin Ma, Shiqian Xue, Lingzhou Optimization and Control This paper proposes a new inexact manifold proximal linear (IManPL) algorithm for solving nonsmooth, nonconvex composite optimization problems over an embedded submanifold. At each iteration, IManPL solves a convex subproblem inexactly, guided by two adaptive stopping criteria. We establish convergence guarantees and show that IManPL achieves the best first-order oracle complexity for solving this class of problems. Numerical experiments on sparse spectral clustering and sparse principal component analysis demonstrate that our methods outperform existing approaches. |
| title | A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.19234 |