  This paper is concerned with the large particle limit for the consensus-based
optimization (CBO), which was postulated in the pioneering works [6,28]. In
order to solve this open problem, we adapt a compactness argument by first
proving the tightness of the empirical measures $\{\mu^N\}_{N\geq 2}$
associated to the particle system and then verifying that the limit measure
$\mu$ is the unique weak solution to the mean-field CBO equation. Such results
are extended to the model of particle swarm optimization (PSO).
