Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications
Abstract
In this paper, we establish well-posedness of reflected McKean-Vlasov SDEs and their particle approximations in smooth non-convex domains. We prove convergence of the interacting particle system to the corresponding mean-field limit with the optimal rate of convergence. We motivate this study with applications to sampling and optimization in constrained domains by considering reflected mean-field Langevin SDEs and two reflected consensus-based optimization (CBO) models, respectively. We utilize reflection coupling to study long-time behaviour of reflected mean-field SDEs and also investigate convergence of the reflected CBO models to the global minimum of a constrained optimization problem. We numerically test reflected CBO models on benchmark constrained optimization problems and an inverse problem.
Keywords
Cite
@article{arxiv.2412.20247,
title = {Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications},
author = {P. D. Hinds and A. Sharma and M. V. Tretyakov},
journal= {arXiv preprint arXiv:2412.20247},
year = {2025}
}