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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.20183 |
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| _version_ | 1866917097805709312 |
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| author | Yin, Yingdong |
| author_facet | Yin, Yingdong |
| contents | This paper generalizes the dynamical system proposed by Wang et al. [Siam. J. Sci. Comput., 2021] to multiobjective optimization by investigating a multiobjective accelerated gradient-like flow with asymptotically vanishing normalized gradient. Using Lyapunov analysis, we obtain convergence rates of $O(1/t^2)$ and $O(\ln^2 t / t^2)$ for the trajectory solution under two distinct parameter selections. Under certain assumptions, we further prove that the trajectory solution of this gradient flow converges to a weak Pareto solution for convex multiobjective optimization problems. Through corresponding discretization, we derive a new class of multiobjective gradient methods achieving a convergence rate of $O(\ln^2 k / k^2)$. Additionally, numerical experiments validate the theoretical results, demonstrating that this gradient flow outperforms other existing dynamical systems in the literature regarding convergence speed, and our algorithm exhibits corresponding advantages. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiobjective Accelerated Gradient-like Flow with Asymptotic Vanishing Normalized Gradient Yin, Yingdong Optimization and Control This paper generalizes the dynamical system proposed by Wang et al. [Siam. J. Sci. Comput., 2021] to multiobjective optimization by investigating a multiobjective accelerated gradient-like flow with asymptotically vanishing normalized gradient. Using Lyapunov analysis, we obtain convergence rates of $O(1/t^2)$ and $O(\ln^2 t / t^2)$ for the trajectory solution under two distinct parameter selections. Under certain assumptions, we further prove that the trajectory solution of this gradient flow converges to a weak Pareto solution for convex multiobjective optimization problems. Through corresponding discretization, we derive a new class of multiobjective gradient methods achieving a convergence rate of $O(\ln^2 k / k^2)$. Additionally, numerical experiments validate the theoretical results, demonstrating that this gradient flow outperforms other existing dynamical systems in the literature regarding convergence speed, and our algorithm exhibits corresponding advantages. |
| title | Multiobjective Accelerated Gradient-like Flow with Asymptotic Vanishing Normalized Gradient |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.20183 |