Global convergence of a non-convex Douglas–Rachford iteration

We establish a region of convergence for the proto-typical non-convex Douglas–Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration Borwein and Sims (Fixed-point algorithms for inverse problems in science and engineering, pp. 93–109, <CitationRef CitationID="CR2">2011</CitationRef>) was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given. Copyright Springer Science+Business Media, LLC. 2013