SIAM Journal on Optimization, Volume 30, Issue 1, Page 542-584, January 2020.
Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas--Rachford algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence results for this algorithm are limited to either convex feasibility or consistent nonconvex feasibility with strong assumptions on the regularity of the underlying sets. Using an analytical framework depending only on metric subregularity and pointwise almost averagedness, we analyze the convergence behavior of DR$\lambda$ for feasibility problems that are both nonconvex and inconsistent. We introduce a new type of regularity of sets, called superregular at a distance, to establish sufficient conditions for local linear convergence of the corresponding sequence. These results subsume and extend existing results for this algorithm.

中文翻译：

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松弛Douglas-Rachford算法的收敛性分析

SIAM优化杂志，第30卷，第1期，第542-584页，2020年1月。
由于非凸性，成像中可行性问题的不一致，在十多年前首次提出了松弛交替平均反射算法或松弛道格拉斯-拉奇福德算法（DR $ \ lambda $）。该算法的收敛结果限于凸可行性或一致非凸可行性，并且对基础集的正则性有很强的假设。使用仅依赖于度量次正则性和逐点几乎平均的分析框架，我们分析了DR $ \ lambda $对于非凸且不一致的可行性问题的收敛行为。我们介绍了一种新型的集正则性，在远处称为超正则集，以为相应序列的局部线性收敛建立充分的条件。