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

2012/11/07 by Heinz H. Bauschke, Bauschke, Heinz H., Jiawei Chen +3
Mathematics · #47H09 (Primary) 52B55 #65K10 #90C25 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #math.FA #math.OC #msc:47H09 #msc:52B55 #msc:65K10 #msc:90C25

paper · pdf · doi:10.48550/arxiv.1211.1639

arxiv created 2012/11/07 · arxiv updated 2012/11/08

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.

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