Convergence analysis of dynamical systems for optimization by an improved Lyapunov framework
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918419451871232 |
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| author | Tabei, Atsushi Tanaka, Ken'ichiro |
| author_facet | Tabei, Atsushi Tanaka, Ken'ichiro |
| contents | We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic constructions of Lyapunov functions for such analysis, while also revealing limitations of the Lyapunov analysis. Aujol--Dossal--Rondepierre (2023) have proposed a technique to address this issue by reorganizing Lyapunov functions so as to evaluate a quantity $f(x(t)) - f_* - g(t)\|x(t)-x_*\|^2$ rather than $f(x(t)) - f_*$. By combining this technique with our computer-assisted framework to discover Lyapunov functions, we develop an improved method that reproduces an existing convergence rate or yields better rates than previous studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29330 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of dynamical systems for optimization by an improved Lyapunov framework Tabei, Atsushi Tanaka, Ken'ichiro Optimization and Control Numerical Analysis 34D05, 65K99, 90C25, 93D30 We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic constructions of Lyapunov functions for such analysis, while also revealing limitations of the Lyapunov analysis. Aujol--Dossal--Rondepierre (2023) have proposed a technique to address this issue by reorganizing Lyapunov functions so as to evaluate a quantity $f(x(t)) - f_* - g(t)\|x(t)-x_*\|^2$ rather than $f(x(t)) - f_*$. By combining this technique with our computer-assisted framework to discover Lyapunov functions, we develop an improved method that reproduces an existing convergence rate or yields better rates than previous studies. |
| title | Convergence analysis of dynamical systems for optimization by an improved Lyapunov framework |
| topic | Optimization and Control Numerical Analysis 34D05, 65K99, 90C25, 93D30 |
| url | https://arxiv.org/abs/2603.29330 |