Adaptive Accelerated Gradient Method for Smooth Convex Optimization
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909974780706816 |
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| author | Wang, Zepeng Peypouquet, Juan |
| author_facet | Wang, Zepeng Peypouquet, Juan |
| contents | We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is assumed unknown, without resorting to line search procedures. The sequence generated by this method converges weakly to a minimizer of the objective function, and the function values converge at a fast rate of $\mathcal{O}\left( \frac{1}{k^2} \right)$. Moreover, if the objective function is strongly convex, the function values converge at a linear rate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_20478 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Accelerated Gradient Method for Smooth Convex Optimization Wang, Zepeng Peypouquet, Juan Optimization and Control We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is assumed unknown, without resorting to line search procedures. The sequence generated by this method converges weakly to a minimizer of the objective function, and the function values converge at a fast rate of $\mathcal{O}\left( \frac{1}{k^2} \right)$. Moreover, if the objective function is strongly convex, the function values converge at a linear rate. |
| title | Adaptive Accelerated Gradient Method for Smooth Convex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2512.20478 |