  The Douglas-Rachford projection algorithm is an iterative method used to find
a point in the intersection of closed constraint sets. The algorithm has been
experimentally observed to solve various nonconvex feasibility problems which
current theory cannot sufficiently explain. In this paper, we prove convergence
of the Douglas-Rachford algorithm in a potentially nonconvex setting. Our
analysis relies on the existence of a Lyapunov-type functional whose convexity
properties are not tantamount to convexity of the original constraint sets.
Moreover, we provide various nonconvex examples in which our framework proves
global convergence of the algorithm.
