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arXiv · 2105.12919

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

Hui Huang·Jinniao Qiu
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Abstract

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).

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Hui Huang, Jinniao Qiu. 2021-05-27. On the mean-field limit for the consensus-based optimization. https://doi.org/10.1002/mma.8279

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