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Hypocoercivity in metastable settings and kinetic simulated annealing

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Abstract

Combining classical arguments for the analysis of the simulated annealing algorithm with the more recent hypocoercive method of distorted entropy, we prove the convergence for large time of the kinetic Langevin annealing with logarithmic cooling schedule.

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Notes

  1. Allowing large steps is not a reasonable solution, since in applied problems the dimension is large and the reasonable configurations (i.e. the points where U is not too large) lie in a very small area in view of the Lebesgue measure. A uniformly-generated jump proposal will always be absurd, and rejected.

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Acknowledgements

The author would like to thank Laurent Miclo, who initiated this work, for numerous fruitful discussions. This work has been supported by EFI Project ANR-17-CE40-0030 of the French National Research Agency (ANR).

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Authors and Affiliations

  1. CERMICS (ENPC), INRIA, Université Paris-Est, 8 Avenue Blaise Pascal, Cité Descartes, 77455, Marne-la-Vallée, France

    Pierre Monmarché

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  1. Pierre Monmarché
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Correspondence to Pierre Monmarché.

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This work has been supported by ANR STAB.

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Monmarché, P. Hypocoercivity in metastable settings and kinetic simulated annealing. Probab. Theory Relat. Fields 172, 1215–1248 (2018). https://doi.org/10.1007/s00440-018-0828-y

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