Global convergence of a non-convex Douglas–Rachford iteration
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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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- 2.Borwein, J.M., Sims, B.: The Douglas–Rachford Algorithm in the Absence of Convexity. In: Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer Optimization and its Applications 49, pp. 93–109 (2011)Google Scholar
- 3.Borwein J.M, Zhu Q.J: Techniques of Variational Analysis. Springer, New York (2005)Google Scholar
- 6.Gravel S., Elser V.: Divide and concur: a general approach constraint satisfaction. Phys. Rev. E 78(036706), 1–5 (2008)Google Scholar