  We aim to improve upon the exploration of the general-purpose random walk
Metropolis algorithm when the target has non-convex support $A \subset
\mathbb{R}^d$, by reusing proposals in $A^c$ which would otherwise be rejected.
The algorithm is Metropolis-class and under standard conditions the chain
satisfies a strong law of large numbers and central limit theorem. Theoretical
and numerical evidence of improved performance relative to random walk
Metropolis are provided. Issues of implementation are discussed and numerical
examples, including applications to global optimisation and rare event
sampling, are presented.
