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

By Hui-Lin Huang, Jinniao Qiu. Mathematical methods in the applied sciences, 2021

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

Subfields: Computer Networks and Communications, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7c0a4da29d4f939e736fe134b8a5ce3a33982ba6