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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2510.16680 |
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| _version_ | 1866918529275527168 |
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| author | Chen, Long Xu, Zeyi |
| author_facet | Chen, Long Xu, Zeyi |
| contents | Two accelerated first-order methods, HNAG$^+$ and HNAG$^{++}$, are presented for smooth strongly convex optimization. By optimizing the coercivity constant of the HNAG flow and using a refined Lyapunov analysis, it is shown that HNAG$^+$ achieves the optimal global rate $1-2/\sqrtκ$, matching the information-theoretic lower bound for strongly convex optimization. For functions with Local Asymptotic Symmetry at the minimizer, HNAG$^{++}$ is shown to achieve the asymptotic rate $1-2\sqrt{2/κ}$, matching the best known asymptotic rate under $\mathcal C^2$ regularity, while applying to a broader local function class. Numerical experiments on linear and nonlinear examples show that the proposed methods are competitive with existing accelerated schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | HNAG$^{++}$: An Accelerated Gradient Method with a Refined Asymptotic Rate for Strongly Convex Optimization Chen, Long Xu, Zeyi Optimization and Control Two accelerated first-order methods, HNAG$^+$ and HNAG$^{++}$, are presented for smooth strongly convex optimization. By optimizing the coercivity constant of the HNAG flow and using a refined Lyapunov analysis, it is shown that HNAG$^+$ achieves the optimal global rate $1-2/\sqrtκ$, matching the information-theoretic lower bound for strongly convex optimization. For functions with Local Asymptotic Symmetry at the minimizer, HNAG$^{++}$ is shown to achieve the asymptotic rate $1-2\sqrt{2/κ}$, matching the best known asymptotic rate under $\mathcal C^2$ regularity, while applying to a broader local function class. Numerical experiments on linear and nonlinear examples show that the proposed methods are competitive with existing accelerated schemes. |
| title | HNAG$^{++}$: An Accelerated Gradient Method with a Refined Asymptotic Rate for Strongly Convex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.16680 |