A Bregman projection method for approximating fixed points of quasi-Bregman nonexpansive mappings

2013/09/25 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.1309.6402

arxiv created 2013/09/25 · arxiv updated 2013/09/26

Abstract

We introduce an abstract algorithm that aims to find the Bregman projection onto a closed convex set. As an application, the asymptotic behaviour of an iterative method for finding a fixed point of a quasi Bregman nonexpansive mapping with the fixed-point closedness property is analyzed. We also show that our result is applicable to Bregman subgradient projectors.

Related

• A projection method for approximating fixed points of quasi nonexpansive mappings without the usual demiclosedness condition
• A New Shrinking projection Algorithm for an infinite family of Bregman weak relatively nonexpansive mappings in a Banach Space
• Alternating Bregman projections and convergence of the EM algorithm
• An iterative algorithm for a common fixed point of Bregman Relatively Nonexpansive Mappings
• A strong convergence theorem for solving an equilibrium problem and a fixed point problem using the Bregman distance