On the local convergence of the Douglas–Rachford algorithm

By Heinz H. Bauschke, Dominikus Noll. 2014

56 citations recorded by the source corpus.

We discuss the Douglas–Rachford algorithm to solve the feasibility problem for two closed sets A,B in $${\mathbb{R}^d}$$Rd . 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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/50e8a4ffd3aee4ddfac75a4d45243719f456310f

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Citations in the corpus

• SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD (2018, background): “In 2014 Bauschke and Noll proved local convergence to a fixed point in the case where A and B are finite unions of convex sets [38].”