  The convergence of the kinetic Langevin simulated annealing is proven under
mild assumptions on the potential $U$ for slow logarithmic cooling schedules.
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 the overdamped
elliptic case, and on precise quantitative high order Sobolev hypocoercive
estimates.
