Simulated annealing of heavy-tailed jump-diffusions
by Ilya Pavlyukevich
Abstract: We consider a one dimensional dynamical system driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a stable symmetric non-Gaussian L'evy process whose scale parameter decreases as a power function of time. It turns out that the limiting behaviour of the perturbed dynamical system is different for slow and fast decrease rates of the noise intensity. As opposed to the well-studied Gaussian case, the limiting probability is not concentrated in the global minimum of U.
Finally, we discuss simulated annealing of jump processes with a
non-constant stability index and consider applications to non-local random search and stochastic optimisation.
For More Information: Kostantin Borovkov K.Borovkov@ms.unimelb.edu.au