Overview
- Studies the approximate solutions of common fixed point problems and convex feasibility problems in the presence of computational errors
- Examines the convergence of component-averaged row projections [CARP]
- Extends results for a dynamic string-averaging version of the proximal algorithm
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Optimization and Its Applications (SOIA, volume 112)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant.
Beginning with an introduction, this monograph moves on to study:
· dynamic string-averaging methods for common fixed point problems in a Hilbert space
· dynamic string methods for common fixed point problems in a metric space<
· dynamic string-averaging version of the proximal algorithm
· common fixed point problems in metric spaces· common fixed point problems in the spaces with distances of the Bregman type
· a proximal algorithm for finding a common zero of a family of maximal monotone operators
· subgradient projections algorithms for convex feasibility problems in Hilbert spaces
Reviews
“The present book on fixed point topics focusses on the study of the convergence of iterative algorithms which are mainly intended to approximate solutions of common fixed point problems and of convex feasibility problems in the presence of computational errors. … The book, including mainly original theoretical contributions of the author to the convergence analysis of the considered iterative algorithms, is addressed to researchers interested in fixed point theory and/or convex feasibility problems.” (Vasile Berinde, zbMATH 1357.49007, 2017)
Authors and Affiliations
Bibliographic Information
Book Title: Approximate Solutions of Common Fixed-Point Problems
Authors: Alexander J. Zaslavski
Series Title: Springer Optimization and Its Applications
DOI: https://doi.org/10.1007/978-3-319-33255-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-33253-6Published: 08 July 2016
Softcover ISBN: 978-3-319-81467-4Published: 30 May 2018
eBook ISBN: 978-3-319-33255-0Published: 30 June 2016
Series ISSN: 1931-6828
Series E-ISSN: 1931-6836
Edition Number: 1
Number of Pages: IX, 454
Topics: Calculus of Variations and Optimal Control; Optimization, Numerical Analysis, Operator Theory