In this work, we propose and analyse two splitting algorithms for finding a zero of the sum of three monotone operators, one of which is assumed to be Lipschitz continuous. Each iteration of these algorithms require one forward evaluation of the Lipschitz continuous operator and one resolvent evaluation of each of the other two operators. By specialising to two operator inclusions, we recover the forward-reflected-backward and the reflected-forward-backward splitting methods as particular cases. The inspiration for the proposed algorithms arises from interpretations of the aforementioned reflected splitting algorithms as discretisations of the continuous-time proximal point algorithm.

中文翻译：

---

三个算子单调内含物的后向-前向-反射-后向分裂

在这项工作中，我们提出并分析了两种分裂算法，用于寻找三个单调算子之和的零，其中一个被假定为 Lipschitz 连续的。这些算法的每次迭代都需要对 Lipschitz 连续算子进行一次前向评估，并对其他两个算子中的每一个进行解析评估。通过专门针对两个算子包含，我们将前向反射后向和反射前向后向分裂方法恢复为特殊情况。所提出算法的灵感来自于将上述反射分裂算法解释为连续时间近端算法的离散化。