Goran Banjac
Published 2020-09-02Version 1
The Douglas-Rachford algorithm can be represented as the fixed point iteration of a firmly nonexpansive operator, which converges to a fixed point, provided it exists. When the operator has no fixed points, the algorithm's iterates diverge, but the difference between consecutive iterates converges to the minimal displacement vector, which can be used to certify infeasibility of an optimization problem. In this paper, we establish new properties of the minimal displacement vector, which allow us to generalize some existing results.
On the order of the operators in the Douglas-Rachford algorithm
The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle
The fixed point iteration of positive concave mappings converges geometrically if a fixed point exists: implications to wireless network problems
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