The Douglas–Rachford method is a splitting method frequently employed for finding zeros of sums of maximally monotone operators. When the operators in question are normal cone operators, the iterated process may be used to solve feasibility problems of the following form: Find $x\in \bigcap _{k=1}^{N}S_{k}$. The success of the method in the context of closed, convex, nonempty sets $S_{1},\ldots ,S_{N}$ is well known and understood from a theoretical standpoint. However, its performance in the nonconvex context is less well understood, yet it is surprisingly impressive. This was particularly compelling to Jonathan M. Borwein who, intrigued by Elser, Rankenburg and Thibault’s success in applying the method to solving sudoku puzzles, began an investigation of his own. We survey the current body of literature on the subject, and we summarize its history. We especially commemorate Professor Borwein’s celebrated contributions to the area.

中文翻译：

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调查：道格拉斯-拉奇福德 60 年

Douglas-Rachford 方法是一种经常用于寻找最大单调算子之和的零点的分裂方法。当所讨论的算子是普通锥算子时，可以使用迭代过程来求解可行性以下形式的问题：查找$x\in \bigcap _{k=1}^{N}S_{k}$. 该方法在闭集、凸集、非空集的上下文中的成功$S_{1},\ldots ,S_{N}$是众所周知的并且从理论的角度来理解。然而，它在非凸环境中的表现却鲜为人知，但却令人惊讶地令人印象深刻。这对 Jonathan M. Borwein 尤其有吸引力，他对 Elser、Rankenburg 和 Thibault 在应用该方法解决数独谜题方面的成功很感兴趣，开始了他自己的调查。我们调查了当前有关该主题的文献，并总结了其历史。我们特别纪念 Borwein 教授对该领域的杰出贡献。