A note on the forward-Douglas–Rachford splitting for monotone inclusion and convex optimization
A note on the forward-Douglas–Rachford splitting for monotone inclusion and convex optimization
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DOI：
10.1007/s11590-018-1272-8
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发表时间：
2017-04
影响因子：
1.6
通讯作者：
Hugo Raguet
中科院分区：
文献类型：
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作者：
Hugo Raguet
我们揭示了结构上的“三个运营商”版本的前向道格拉斯-Rachford分裂算法找到一个零的总和最大单调运营商，其中B是cocoercive，只涉及计算的带的预解式的A和C，分别。我们表明，这是一个简单的扩展，我们提出的不动点算法作为一个推广的向前向后分裂算法，最初设计用于寻找一个零的任意数量的最大单调算子，其中B是cocoercive的总和，只涉及计算的带的预解式的每一个分别。我们认为，前者是“真正的”前向道格拉斯-Rachford分裂算法，在文献中最初使用这个名称。然后，我们突出的扩展到任意数量的最大单调算子的分裂，在一个配方承认预处理算子。最后，我们实验证明其兴趣的上下文中的非光滑凸优化。
We shed light on the structure of the “three-operator” version of the forward-Douglas–Rachford splitting algorithm for finding a zero of a sum of maximally monotone operators, whereBis cocoercive, involving only the computation ofBand of the resolvent ofAand ofC, separately. We show that it is a straightforward extension of a fixed-point algorithm proposed by us as a generalization of the forward–backward splitting algorithm, initially designed for finding a zero of a sum of an arbitrary number of maximally monotone operators, whereBis cocoercive, involving only the computation ofBand of the resolvent of eachseparately. We argue that, the former is the “true” forward-Douglas–Rachford splitting algorithm, in contrast to the initial use of this designation in the literature. Then, we highlight the extension to an arbitrary number of maximally monotone operators in the splitting,, in a formulation admitting preconditioning operators. We finally demonstate experimentally its interest in the context of nonsmooth convex optimization.