论文标题
三个操作员单调包含物
Backward-Forward-Reflected-Backward Splitting for Three Operator Monotone Inclusions
论文作者
论文摘要
在这项工作中，我们提出并分析了两种分裂算法，以找到三个单调算子的总和中的零，其中一个被认为是Lipschitz的连续。这些算法的每一次迭代都需要对Lipschitz连续操作员进行一个前瞻性评估，并对其他两个操作员中的每个运算符进行回避评估。通过专门针对两个操作员夹杂物，我们恢复了向前反向的回避，并作为特定情况将反射的反向拆分方法作为特殊情况。所提出算法的灵感来自对上述反映的分裂算法作为连续时间近端算法的离散算法的解释。
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.
