Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications
Artikel i vetenskaplig tidskrift, 2025

In this paper, we establish well-posedness of reflected McKean-Vlasov stochastic differential equations (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 for sampling and two reflected consensus-based optimization (CBO) models. We utilize reflection coupling to study long-time behavior 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.

mean-field Langevin dynamics

Interacting particle system

reflected stochastic differential equations

consensus-based optimization

reflected mean-field diffusion

propagation of chaos

constrained sampling

constrained optimization

Författare

Piers D. Hinds

University of Nottingham

Akash Sharma

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Michael V. Tretyakov

University of Nottingham

Mathematical Models and Methods in Applied Sciences

0218-2025 (ISSN) 17936314 (eISSN)

Vol. 35 8 1845-1887

Ämneskategorier (SSIF 2025)

Sannolikhetsteori och statistik

DOI

10.1142/S0218202525500241

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Senast uppdaterat

2025-06-14