On the order of the operators in the Douglas-Rachford algorithm

Heinz H. Bauschke; Walaa M. Moursi

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arXiv · 1505.02796

On the order of the operators in the Douglas-Rachford algorithm

Heinz H. Bauschke·Walaa M. Moursi

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Abstract

The Douglas-Rachford algorithm is a popular method for finding zeros of sums of monotone operators. By its definition, the Douglas-Rachford operator is not symmetric with respect to the order of the two operators. In this paper we provide a systematic study of the two possible Douglas-Rachford operators. We show that the reflectors of the underlying operators act as bijections between the fixed points sets of the two Douglas-Rachford operators. Some elegant formulae arise under additional assumptions. Various examples illustrate our results.

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Heinz H. Bauschke, Walaa M. Moursi. 2015-05-11. On the order of the operators in the Douglas-Rachford algorithm. https://arxiv.org/abs/1505.02796

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