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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.27156 |
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| _version_ | 1866908622501445632 |
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| author | Long, Xian-Jun Zeng, Kang Li, Gao-Xi Dao, Minh N. Peng, Zai-Yun |
| author_facet | Long, Xian-Jun Zeng, Kang Li, Gao-Xi Dao, Minh N. Peng, Zai-Yun |
| contents | In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques with first-order methods, we propose a variable smoothing alternating proximal gradient algorithm that features flexible parameter choices for step sizes and smoothing levels. Under mild assumptions, we establish that the iteration complexity to reach an $\varepsilon$-approximate stationary point is $\mathcal{O}(\varepsilon^{-3})$. The proposed algorithm is evaluated on sparse signal recovery and image denoising problems. Numerical experiments demonstrate its effectiveness and superiority over existing algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27156 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variable Smoothing Alternating Proximal Gradient Algorithm for Coupled Composite Optimization Long, Xian-Jun Zeng, Kang Li, Gao-Xi Dao, Minh N. Peng, Zai-Yun Optimization and Control In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques with first-order methods, we propose a variable smoothing alternating proximal gradient algorithm that features flexible parameter choices for step sizes and smoothing levels. Under mild assumptions, we establish that the iteration complexity to reach an $\varepsilon$-approximate stationary point is $\mathcal{O}(\varepsilon^{-3})$. The proposed algorithm is evaluated on sparse signal recovery and image denoising problems. Numerical experiments demonstrate its effectiveness and superiority over existing algorithms. |
| title | Variable Smoothing Alternating Proximal Gradient Algorithm for Coupled Composite Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.27156 |