  In this paper, we consider sampling from a class of distributions with thin
tails supported on $\mathbb{R}^d$ and make two primary contributions. First, we
propose a new Metropolized Algorithm With Optimization Step (MAO), which is
well suited for such targets. Our algorithm is capable of sampling from
distributions where the Metropolis-adjusted Langevin algorithm (MALA) is not
converging or lacking in theoretical guarantees. Second, we derive upper bounds
on the mixing time of MAO. Our results are supported by simulations on multiple
target distributions.
