학술논문
Demiclosedness principles for generalized nonexpansive mappings.
Document Type
Journal
Author
Bartz, Sedi (1-MAL) AMS Author Profile; Campoy, Rubén (1-MAL) AMS Author Profile; Phan, Hung M. (1-MAL) AMS Author Profile
Source
Subject
47 Operator theory -- 47J Equations and inequalities involving nonlinear operators
47J25Iterative procedures
49Calculus of variations and optimal control; optimization -- 49M Numerical methods
49M27Decomposition methods
47J25
49
49M27
Language
English
Abstract
The authors provide extensions of the demiclosedness principle, which are compatible with the framework of more general families of mappings such as cocoercive and conically averaged mappings. As an application, they derive the weak convergence of the shadow sequence generated by an adaptive Douglas-Rachford algorithm. In particular, the corresponding resolvents in the adaptive Douglas-Rachford algorithm are not necessarily firmly nonexpansive.