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, 2011) was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given.
KeywordsNon-convex feasibility problem Fixed point theory Projection algorithm Douglas–Rachford algorithm Global convergence Signal reconstruction
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