Heinz H. Bauschke, Walaa M. Moursi
Published 2015-04-14Version 1
The Douglas--Rachford algorithm is a classical and very successful splitting method for finding the zeros of the sums of monotone operators. When the underlying operators are normal cone operators, the algorithm solves a convex feasibility problem. In this paper, we provide a detailed study of the Douglas--Rachford iterates and the corresponding {shadow sequence} when the sets are affine subspaces that do not necessarily intersect. We prove strong convergence of the shadows to the nearest generalized solution. Our results extend recent work from the consistent to the inconsistent case. Various examples are provided to illustrates the results.
On the Douglas--Rachford algorithm
The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle
On the order of the operators in the Douglas-Rachford algorithm
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