论文标题
广义非专业映射的解密原则
Demiclosedness principles for generalized nonexpansive mappings
论文作者
论文摘要
解脱性原理是研究迭代方法收敛性的强大工具。例如，牢固的非专用映射的多手术原理对于获得Douglas-Rachford算法产生的阴影序列的弱收敛性的简单和透明的参数很有用。我们提供了该原理的扩展，该原则与更普遍的映射属于诸如cocoercive和圆锥形平均映射的框架的框架兼容。作为应用程序，我们得出了由自适应Douglas-Rachford算法产生的阴影序列的弱收敛性。
Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments for the weak convergence of the shadow sequence generated by the Douglas-Rachford algorithm. We provide extensions of this principle which are compatible with the framework of more general families of mappings such as cocoercive and conically averaged mappings. As an application, we derive the weak convergence of the shadow sequence generated by the adaptive Douglas-Rachford algorithm.
