Accelerated Gradient Methods via Inertial Systems with Hessian-driven Damping
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912243909656576 |
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| author | Wang, Zepeng Peypouquet, Juan |
| author_facet | Wang, Zepeng Peypouquet, Juan |
| contents | We analyze the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system with Hessian-driven damping. We recover a convergence rate, up to a factor of 2 speedup upon Nesterov's scheme, for smooth strongly convex functions. As a byproduct of our analyses, we also derive linear convergence rates for convex functions satisfying quadratic growth condition or Polyak-Łojasiewicz inequality. As a significant feature of our results, the dependence of the convergence rate on parameters of the inertial system/algorithm is revealed explicitly. This may help one get a better understanding of the acceleration mechanism underlying an inertial algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accelerated Gradient Methods via Inertial Systems with Hessian-driven Damping Wang, Zepeng Peypouquet, Juan Optimization and Control We analyze the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system with Hessian-driven damping. We recover a convergence rate, up to a factor of 2 speedup upon Nesterov's scheme, for smooth strongly convex functions. As a byproduct of our analyses, we also derive linear convergence rates for convex functions satisfying quadratic growth condition or Polyak-Łojasiewicz inequality. As a significant feature of our results, the dependence of the convergence rate on parameters of the inertial system/algorithm is revealed explicitly. This may help one get a better understanding of the acceleration mechanism underlying an inertial algorithm. |
| title | Accelerated Gradient Methods via Inertial Systems with Hessian-driven Damping |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2502.16953 |