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arXiv · 2302.09504

On Douglas-Rachford splitting that generally fails to be a proximal mapping: A degenerate proximal point analysis

Feng Xue
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Abstract

Based on a degenerate proximal point analysis, we show that the Douglas-Rachford splitting can be reduced to a well-defined resolvent, but generally fails to be a proximal mapping. This extends the recent result of [Bauschke, Schaad and Wang. Math. Program., 168 (2018), pp. 55-61] to more general setting. The related concepts and consequences are also discussed. In particular, the results regarding the maximal and cyclic monotonicity are instrumental for analyzing many operator splitting algorithms.

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Feng Xue. 2023-02-19. On Douglas-Rachford splitting that generally fails to be a proximal mapping: A degenerate proximal point analysis. https://arxiv.org/abs/2302.09504

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