Global convergence of a non-convex Douglas–Rachford iteration

1. Bauschke H.H, Combettes P.L, Luke D.R: Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization. J. Opt. Soc. Am. A 19(7), 1334–1345 (2002)

   Article  Google Scholar 

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)

3. Borwein J.M, Zhu Q.J: Techniques of Variational Analysis. Springer, New York (2005)

   Google Scholar 

4. Elser V., Rankenburg I., Thibault P.: Searching with iterated maps. Proc. Natl. Acad. Sci. 104, 418–423 (2007)

   Article  Google Scholar 

5. Goebel K., Kirk W.A: Topics in Metric Fixed Point Theory. Cambridge University Press, Cambridge (1990)

   Book  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 

7. Lions P.L, Mercier B.: Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16(6), 964–979 (1979)

   Article  Google Scholar 

8. Opial Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Am. Math. Soc. 73, 591–597 (1967)

   Article  Google Scholar 

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