论文标题
加强计算分解的分裂方法
Strengthened Splitting Methods for Computing Resolvents
论文作者
论文摘要
在这项工作中，我们开发了一个系统的框架，用于计算两个或多个单调运算符的总和的分解，该总和仅在单独激活总和中的每个操作员。该框架开发的关键工具是设定值运算符的“加强”的概念，可以将其视为保留计算障碍的一种正则化。通过此框架得出了许多迭代方案后，我们演示了它们在最佳近似问题，图像降解和椭圆形PDE中的应用。
In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each operator in the sum individually. The key tool in the development of this framework is the notion of the "strengthening" of a set-valued operator, which can be viewed as a type of regularisation that preserves computational tractability. After deriving a number of iterative schemes through this framework, we demonstrate their application to best approximation problems, image denoising and elliptic PDEs.
