JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
Essential convergence rate of ordinary differential equations appearing in optimization
Kansei UshiyamaShun SatoTakayasu Matsuo
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2022 年 14 巻 p. 119-122

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Some continuous optimization methods can be connected to ordinary differential equations (ODEs) by taking continuous limits, and their convergence rates can be explained by the ODEs. However, since such ODEs can achieve any convergence rate by time rescaling, the correspondence is not as straightforward as usually expected, and deriving new methods through ODEs is not quite direct. In this letter, we pay attention to stability restriction in discretizing ODEs and show that acceleration by time rescaling basically implies deceleration in discretization; they balance out so that we can define an attainable unique convergence rate which we call ``essential convergence rate''.

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© 2022, The Japan Society for Industrial and Applied Mathematics
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