English

A projection method for approximating fixed points of quasi nonexpansive mappings without the usual demiclosedness condition

Functional Analysis 2012-11-08 v1 Optimization and Control

Abstract

We introduce and analyze an abstract algorithm that aims to find the projection onto a closed convex subset of a Hilbert space. When specialized to the fixed point set of a quasi nonexpansive mapping, the required sufficient condition (termed "fixed-point closed") is less restrictive than the usual conditions based on the demiclosedness principle. A concrete example of a subgradient projector is presented which illustrates the applicability of this generalization.

Keywords

Cite

@article{arxiv.1211.1639,
  title  = {A projection method for approximating fixed points of quasi nonexpansive mappings without the usual demiclosedness condition},
  author = {Heinz H. Bauschke and Jiawei Chen and Xianfu Wang},
  journal= {arXiv preprint arXiv:1211.1639},
  year   = {2012}
}