Simulated Annealing In ${\mathbf{R}}^d$ With Slowly Growing Potentials

Abstract

We use a localization procedure to weaken the growth assumptions of Royer [8], Miclo [4] and Zitt [9] concerning the continuous-time simulated annealing in ${\mathbf{R}}^d$. We show that a transition occurs for potentials growing like $a\log \log |x|$ at infinity. We also study a class of potentials with possibly unbounded sets of local minima.

15 pages