Accelerated Proximal Gradient Method with Backtracking for Multiobjective Optimization
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908172854231040 |
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| author | Huang, Chengzhi Chen, Jian Tang, Liping |
| author_facet | Huang, Chengzhi Chen, Jian Tang, Liping |
| contents | This paper proposes a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy focuses on solving the problem of Lipschitz constant being unknown. It allows estimate parameter updates non-increasingly. Furthermore, the proposed strategy effectively avoids the limitation in convergence proofs arising from the non-negativity of the auxiliary sequence, thus providing a theoretical guarantee for its performance. We demonstrate that, under relatively mild assumptions, the algorithm achieves the convergence rate of $O(1/k2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Accelerated Proximal Gradient Method with Backtracking for Multiobjective Optimization Huang, Chengzhi Chen, Jian Tang, Liping Optimization and Control This paper proposes a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy focuses on solving the problem of Lipschitz constant being unknown. It allows estimate parameter updates non-increasingly. Furthermore, the proposed strategy effectively avoids the limitation in convergence proofs arising from the non-negativity of the auxiliary sequence, thus providing a theoretical guarantee for its performance. We demonstrate that, under relatively mild assumptions, the algorithm achieves the convergence rate of $O(1/k2)$. |
| title | Accelerated Proximal Gradient Method with Backtracking for Multiobjective Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.14007 |