{"ID":2889889,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.20183","arxiv_id":"2507.20183","title":"Multiobjective Accelerated Gradient-like Flow with Asymptotic Vanishing Normalized Gradient","abstract":"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.","short_abstract":"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(\\...","url_abs":"https://arxiv.org/abs/2507.20183","url_pdf":"https://arxiv.org/pdf/2507.20183v3","authors":"[\"Yingdong Yin\"]","published":"2025-07-27T09:01:09Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}