  Motivated by nonconvex, inconsistent feasibility problems in imaging, the
relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford
algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence
results for this algorithm are limited either to convex feasibility or
consistent nonconvex feasibility with strong assumptions on the regularity of
the underlying sets. Using an analytical framework depending only on metric
subregularity and pointwise almost averagedness, we analyze the convergence
behavior of DR$\lambda$ for feasibility problems that are both nonconvex and
inconsistent. We introduce a new type of regularity of sets, called
super-regular at a distance, to establish sufficient conditions for local
linear convergence of the corresponding sequence. These results subsume and
extend existing results for this algorithm.
