Fast convex optimization via inertial systems with asymptotically vanishing viscosity and Hessian-driven damping
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916847375351808 |
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| author | Wang, Zepeng Peypouquet, Juan |
| author_facet | Wang, Zepeng Peypouquet, Juan |
| contents | We study the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system combining asymptotic vanishing viscous and Hessian-driven damping. We establish a fast sublinear convergence rate in case the objective function is convex and satisfies Polyak-Łojasiewicz inequality. We also establish a linear convergence rate for strongly convex functions. The results can provide more insights into the convergence property of Nesterov's accelerated gradient method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21730 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast convex optimization via inertial systems with asymptotically vanishing viscosity and Hessian-driven damping Wang, Zepeng Peypouquet, Juan Optimization and Control We study the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system combining asymptotic vanishing viscous and Hessian-driven damping. We establish a fast sublinear convergence rate in case the objective function is convex and satisfies Polyak-Łojasiewicz inequality. We also establish a linear convergence rate for strongly convex functions. The results can provide more insights into the convergence property of Nesterov's accelerated gradient method. |
| title | Fast convex optimization via inertial systems with asymptotically vanishing viscosity and Hessian-driven damping |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.21730 |