Abstract
The convergence of the kinetic langevin simulated annealing is proven under mild assumptions on the potential U for slow logarithmic cooling schedules, which widely extends the scope of the previous results of [14]. Moreover, non-convergence for fast logarithmic and non-logarithmic cooling schedules is established. The results are based on an adaptation to non-elliptic non-reversible kinetic settings of a localization/local convergence strategy developed by Fournier and Tardif in [6] in the overdamped elliptic case, and on precise quantitative high order Sobolev hypocoercive estimates.
Acknowledgments
This work has been partially funded by the French ANR grants EFI (ANR-17-CE40-0030) and SWIDIMS (ANR-20-CE40-0022). P. Monmarché thanks Laurent Dietrich for his help in the proof of Lemma ??. The authors thank Martin Chak for pointing out an error in an earlier version of Lemma ??.
Citation
Lucas Journel. Pierre Monmarché. "Convergence of the kinetic annealing for general potentials." Electron. J. Probab. 27 1 - 37, 2022. https://doi.org/10.1214/22-EJP891
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