# A consensus-based model for global optimization and its mean-field limit

arXiv: https://arxiv.org/abs/1604.05648 · HTML: https://mlsanity.com/paper/1604.05648/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2016.

## Built on by (most cited first, 21 of 21)

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- [Bridging Spherical Black-Box Optimizers](https://mlsanity.com/paper/2606.25761/) (2026)

## Abstract (arXiv)

We introduce a novel first-order stochastic swarm intelligence (SI) model in the spirit of consensus formation models, namely a consensus-based optimization (CBO) algorithm, which may be used for the global optimization of a function in multiple dimensions. The CBO algorithm allows for passage to the mean-field limit, which results in a nonstandard, nonlocal, degenerate parabolic partial differential equation (PDE). Exploiting tools from PDE analysis we provide convergence results that help to understand the asymptotic behavior of the SI model. We further present numerical investigations underlining the feasibility of our approach.