标题： 适定性与反射麦考恩-瓦拉夫随机微分方程的逼近及其应用 显示英文标题

标题： Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications

摘要： 在本文中，我们在光滑非凸域中建立了反射麦考恩-弗拉索夫随机微分方程及其粒子近似问题的适定性。我们证明了相互作用粒子系统以最优收敛率收敛到相应的平均场极限。我们通过考虑反射平均场朗之万随机微分方程和两个反射共识基础优化（CBO）模型，分别以采样和约束域中的优化为应用来激发这项研究。我们利用反射耦合来研究反射平均场随机微分方程的长时间行为，并进一步研究反射CBO模型收敛到约束优化问题全局最小值的情况。我们在基准约束优化问题和一个逆问题上对反射CBO模型进行了数值测试。 显示英文摘要

摘要： 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.