Well-posedness and mean-field limit estimate of a consensus-based algorithm for min-max problems
Optimization and Control
2026-02-16 v1
Abstract
The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the mean-field law. This paper aims to address the theoretical gaps in arXiv:2407.17373, specifically by providing a quantitative estimate of the mean-field limit with respect to the number of particles, as well as establishing the well-posedness of both the finite particle model and the corresponding mean-field dynamics.
Cite
@article{arxiv.2602.12886,
title = {Well-posedness and mean-field limit estimate of a consensus-based algorithm for min-max problems},
author = {Hui Huang and Jethro Warnett},
journal= {arXiv preprint arXiv:2602.12886},
year = {2026}
}
Comments
Main body is 28 pages long. arXiv admin note: text overlap with arXiv:2505.13632