The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914126229405696 |
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| author | Bot, Radu Ioan Fadili, Jalal Nguyen, Dang-Khoa |
| author_facet | Bot, Radu Ioan Fadili, Jalal Nguyen, Dang-Khoa |
| contents | In this paper, we prove that the iterates of the accelerated Nesterov's algorithm in the critical regime do converge in the weak topology to a global minimizer of an $L$-smooth function in a real Hilbert space, hence answering positively a conjecture posed by H. Attouch and co-authors a decade ago. This result is the algorithmic case of a very recent result on the continuous-time system posted by E. Ryu on X, with assistance from ChatGPT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22715 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes Bot, Radu Ioan Fadili, Jalal Nguyen, Dang-Khoa Optimization and Control In this paper, we prove that the iterates of the accelerated Nesterov's algorithm in the critical regime do converge in the weak topology to a global minimizer of an $L$-smooth function in a real Hilbert space, hence answering positively a conjecture posed by H. Attouch and co-authors a decade ago. This result is the algorithmic case of a very recent result on the continuous-time system posted by E. Ryu on X, with assistance from ChatGPT. |
| title | The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.22715 |