Linear convergence of the generalized Douglas-Rachford algorithm for feasibility problems

Abstract

In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically, we establish several local linear convergence results for the algorithm in solving feasibility problems with finitely many closed possibly nonconvex sets under different assumptions. Our findings not only relax some regularity conditions but also improve linear convergence rates in the literature. In the presence of convexity, the linear convergence is global.

References in corpus (3)

• Quantitative convergence analysis of iterated expansive, set-valued mappings
• A Lyapunov-type approach to convergence of the Douglas-Rachford algorithm
• On the finite convergence of the Douglas-Rachford algorithm for solving (not necessarily convex) feasibility problems in Euclidean spaces

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