A remark on the convergence of the Douglas-Rachford iteration in a   non-convex setting
  Using the construction of a Lyapunov function, it is shown that the Douglas-Rachford iteration with respect to a sphere and a line in $\mathbb R^d$ is robustly $\mathcal{KL}$-stable. This implies a convergence which is stronger than uniform convergence on compact sets. 
Ohad Giladi
math.OC