Distributed computation of fixed points of \(\infty\)-nonexpansive maps
type: Item
instance of: scholarly article
title: Distributed computation of fixed points of \(\infty\)-nonexpansive maps
zbMATH Open document ID: 0863.65027
DOI: 10.1007/BF02867437
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1997-01-19T00:00:00Z
review text: The paper deals with a distributed implementation of an algorithm for finding a fixed point of a \(\text{map }F: \mathbb{R}^d\to \mathbb{R}^d\) which is nonexpansive with respect to the \(\infty\)-norm. It is proved that the proposed algorithm converges to the set of fixed points under general conditions. Finally, it is shown that numerical analysis and optimization problems such as shortest path problems, Markov decision processes, systems of linear equations, strictly convex network flow problems can be cast as problems of finding fixed points of \(\infty\)-nonexpansive maps.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65Y10
Mathematics Subject Classification ID: 68W15
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 955212
zbMATH Keywords: algorithm
zbMATH Keywords: fixed point
zbMATH Keywords: shortest path problems
zbMATH Keywords: Markov decision processes
zbMATH Keywords: systems of linear equations
zbMATH Keywords: strictly convex network flow problems
zbMATH Keywords: nonexpansive maps
author: Vivek Borkar
reviewed by: Florica Luban
MaRDI profile type: Publication
cites work: Q4001523
cites work: Q3999474
cites work: Managing interprocessor delays in distributed recursive algorithms
cites work: An analog scheme for fixed-point computation-Part II: Applications
cites work: Q4114574
full work available at URL: https://doi.org/10.1007/bf02867437
OpenAlex ID: W2064782005
description: scientific article; zbMATH DE number 955212