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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.04491 |
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| _version_ | 1866912180343930880 |
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| author | Zhao, Yanan Dong, Qiaoli Zhao, Yufei Wu, Chunlin |
| author_facet | Zhao, Yanan Dong, Qiaoli Zhao, Yufei Wu, Chunlin |
| contents | We consider to design a new efficient and easy-to-implement algorithm to solve a general group sparse optimization model with a class of non-convex non-Lipschitz regularizations, named as fast iterative thresholding and support-and-scale shrinking algorithm (FITS3). In this paper we focus on the case of a least-squares fidelity. FITS3 is designed from a lower bound theory of such models and by integrating thresholding operation, linearization and extrapolation techniques. The FITS3 has two advantages. Firstly, it is quite efficient and especially suitable for large-scale problems, because it adopts support-and-scale shrinking and does not need to solve any linear or nonlinear system. For two important special cases, the FITS3 contains only simple calculations like matrix-vector multiplication and soft thresholding. Secondly, the FITS3 algorithm has a sequence convergence guarantee under proper assumptions. The numerical experiments and comparisons to recent existing non-Lipschitz group recovery algorithms demonstrate that, the proposed FITS3 achieves similar recovery accuracies, but costs only around a half of the CPU time by the second fastest compared algorithm for median or large-scale problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A fast iterative thresholding and support-and-scale shrinking algorithm (fits3) for non-lipschitz group sparse optimization (i): the case of least-squares fidelity Zhao, Yanan Dong, Qiaoli Zhao, Yufei Wu, Chunlin Optimization and Control We consider to design a new efficient and easy-to-implement algorithm to solve a general group sparse optimization model with a class of non-convex non-Lipschitz regularizations, named as fast iterative thresholding and support-and-scale shrinking algorithm (FITS3). In this paper we focus on the case of a least-squares fidelity. FITS3 is designed from a lower bound theory of such models and by integrating thresholding operation, linearization and extrapolation techniques. The FITS3 has two advantages. Firstly, it is quite efficient and especially suitable for large-scale problems, because it adopts support-and-scale shrinking and does not need to solve any linear or nonlinear system. For two important special cases, the FITS3 contains only simple calculations like matrix-vector multiplication and soft thresholding. Secondly, the FITS3 algorithm has a sequence convergence guarantee under proper assumptions. The numerical experiments and comparisons to recent existing non-Lipschitz group recovery algorithms demonstrate that, the proposed FITS3 achieves similar recovery accuracies, but costs only around a half of the CPU time by the second fastest compared algorithm for median or large-scale problems. |
| title | A fast iterative thresholding and support-and-scale shrinking algorithm (fits3) for non-lipschitz group sparse optimization (i): the case of least-squares fidelity |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.04491 |