Multiobjective Balanced Gradient Flow: A Dynamical Perspective on a Class of Optimization Algorithms
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866908499895648256 |
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| author | Yin, Yingdong |
| author_facet | Yin, Yingdong |
| contents | This paper proposes a novel dynamical system called the Multiobjective Balanced Gradient Flow (MBGF), offering a dynamical perspective for normalized gradient methods in a class of multi-objective optimization problems. Under certain assumptions, we prove the existence of solutions for MBGF trajectories and establish their convergence to weak Pareto points in the case of convex objective functions. For both convex and non-convex scenarios, we provide convergence rates of $O(1/t)$ and $O(1/\sqrt{t})$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiobjective Balanced Gradient Flow: A Dynamical Perspective on a Class of Optimization Algorithms Yin, Yingdong Optimization and Control This paper proposes a novel dynamical system called the Multiobjective Balanced Gradient Flow (MBGF), offering a dynamical perspective for normalized gradient methods in a class of multi-objective optimization problems. Under certain assumptions, we prove the existence of solutions for MBGF trajectories and establish their convergence to weak Pareto points in the case of convex objective functions. For both convex and non-convex scenarios, we provide convergence rates of $O(1/t)$ and $O(1/\sqrt{t})$, respectively. |
| title | Multiobjective Balanced Gradient Flow: A Dynamical Perspective on a Class of Optimization Algorithms |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.01775 |