  We introduce a novel first-order stochastic swarm intelligence (SI) model in
the spirit of consensus formation models, namely a consensus-based optimization
(CBO) algorithm, which may be used for the global optimization of a function in
multiple dimensions. The CBO algorithm allows for passage to the mean-field
limit, which results in a nonstandard, nonlocal, degenerate parabolic partial
differential equation (PDE). Exploiting tools from PDE analysis we provide
convergence results that help to understand the asymptotic behavior of the SI
model. We further present numerical investigations underlining the feasibility
of our approach.
