  We introduce a new consensus based optimization (CBO) method where
interacting particle system is driven by jump-diffusion stochastic differential
equations. We study well-posedness of the particle system as well as of its
mean-field limit. The major contributions of this paper are proofs of
convergence of the interacting particle system towards the mean-field limit and
convergence of a discretized particle system towards the continuous-time
dynamics in the mean-square sense. We also prove convergence of the mean-field
jump-diffusion SDEs towards global minimizer for a large class of objective
functions. We demonstrate improved performance of the proposed CBO method over
earlier CBO methods in numerical simulations on benchmark objective functions.
