论文标题
禁食和分散的解析分裂由非专业操作员定义
Frugal and Decentralised Resolvent Splittings Defined by Nonexpansive Operators
论文作者
论文摘要
节俭的分解分组是一类固定点算法，用于在有限的许多设置值单调运算符的总和中找到零，在该总和中，固定点运算符仅使用矢量添加，标量乘法和每个单声酮操作员的分解。在文献中，这些方案的收敛分析是以效率低下的算法为基础进行的。在这项工作中，我们通过为节俭的分解分裂开发一般框架来解决这一问题，该框架同时涵盖并扩展了文献中的几个重要方案。该框架还产生了一种新的分解算法，该算法适用于常规网络上的分散实现。
Frugal resolvent splittings are a class of fixed point algorithms for finding a zero in the sum of the sum of finitely many set-valued monotone operators, where the fixed point operator uses only vector addition, scalar multiplication and the resolvent of each monotone operator once per iteration. In the literature, the convergence analyses of these schemes are performed in an inefficient, algorithm-by-algorithm basis. In this work, we address this by developing a general framework for frugal resolvent splitting which simultaneously covers and extends several important schemes in the literature. The framework also yields a new resolvent splitting algorithm which is suitable for decentralised implementation on regular networks.
