Abstract. We discuss the Douglas-Rachford algorithm to solve the feasibility problem for two closed sets A, B in R d . We prove its local convergence to a fixed point when A, B are finite unions of convex sets. We also show that for more general nonconvex sets the scheme may fail to converge and start to cycle, and may then even fail to solve the feasibility problem.
This is the case of REF , for instance, where A and B are finite unions of convex sets.
On the local convergence of the Douglas-Rachford algorithm
Archiv der Mathematik
Mathematics