On the mean‐field limit for the consensus‐based optimization

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