About stochastic swarm algorithms

Simulated annealing is one of the few generic algorithms enabling us to approximate the set of global minima of a given function.
Unfortunately its convergence is quite slow. A traditional way to by-pass this drawback is to use a large number of independent particles
following this stochastic dynamic.
The goal of the talk is to show how to make them interact in order to get a faster convergence.
Heuristically, any particule will increase its volatility if there are too few or too many particles surrounding it.
While the approach is general, for the moment we only proved the convergence of the corresponding mean field limit in dimension 1.
We will also discuss its gradient flow interpretation in the Wasserstein space, as well as its relation with porous media/fast diffusion evolution equation.

Joint work with Jérôme Bolte and Stéphane Villeneuve.