In this study, we investigate the performance of the Metropolis-adjusted Langevin algorithm in a setting with constraints on the support of the target distribution. We provide a rigorous analysis of the resulting Markov chain, establishing its convergence and deriving an upper bound for its mixing time. Our results demonstrate that the Metropolis-adjusted Langevin algorithm is highly effective in handling this challenging situation: the mixing time bound we obtain is superior to the best known bounds for competing algorithms without an accept-reject step. Our numerical experiments support these theoretical findings, indicating that the Metropolis-adjusted Langevin algorithm shows promising performance when dealing with constraints on the support of the target distribution.

翻译：本研究探讨了Metropolis-adjusted Langevin算法在目标分布支撑集存在约束条件下的表现。我们对所得马尔可夫链进行了严谨分析，证明了其收敛性并推导出混合时间的上界。结果表明，Metropolis-adjusted Langevin算法在处理这一复杂情形时具有显著效能：所获混合时间界限优于已知不含接受-拒绝步骤的竞争算法的最佳界限。数值实验验证了这些理论发现，表明Metropolis-adjusted Langevin算法在处理目标分布支撑集约束时展现出良好的性能表现。