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arXiv · 2004.13778

Demiclosedness principles for generalized nonexpansive mappings

Sedi Bartz·Rubén Campoy·Hung M. Phan
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Abstract

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.

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Sedi Bartz, Rubén Campoy, Hung M. Phan. 2020-04-28. Demiclosedness principles for generalized nonexpansive mappings. https://arxiv.org/abs/2004.13778

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