  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.
