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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2203.12199 |
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| _version_ | 1866929273693011968 |
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| author | Liu, Hailiang Tian, Xuping |
| author_facet | Liu, Hailiang Tian, Xuping |
| contents | This paper investigates a novel gradient algorithm, AGEM, using both energy and momentum, for addressing general non-convex optimization problems. The solution properties of the AGEM algorithm, including aspects such as uniformly boundedness and convergence to critical points, are examined. The dynamic behavior is studied through a comprehensive analysis of a high-resolution ODE system. This ODE system, being nonlinear, is derived by taking the limit of the discrete scheme while preserving the momentum effect through a rescaling of the momentum parameter. The paper emphasizes the global well-posedness of the ODE system and the time-asymptotic convergence of solution trajectories. Furthermore, we establish a linear convergence rate for objective functions that adhere to the Polyak-Łojasiewicz condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_12199 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dynamic behavior for a gradient algorithm with energy and momentum Liu, Hailiang Tian, Xuping Optimization and Control Classical Analysis and ODEs 65K10 (Primary) 90C15 (Secondary) This paper investigates a novel gradient algorithm, AGEM, using both energy and momentum, for addressing general non-convex optimization problems. The solution properties of the AGEM algorithm, including aspects such as uniformly boundedness and convergence to critical points, are examined. The dynamic behavior is studied through a comprehensive analysis of a high-resolution ODE system. This ODE system, being nonlinear, is derived by taking the limit of the discrete scheme while preserving the momentum effect through a rescaling of the momentum parameter. The paper emphasizes the global well-posedness of the ODE system and the time-asymptotic convergence of solution trajectories. Furthermore, we establish a linear convergence rate for objective functions that adhere to the Polyak-Łojasiewicz condition. |
| title | Dynamic behavior for a gradient algorithm with energy and momentum |
| topic | Optimization and Control Classical Analysis and ODEs 65K10 (Primary) 90C15 (Secondary) |
| url | https://arxiv.org/abs/2203.12199 |