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Springer Optimization and Its Applications

Approximate Solutions of Common Fixed-Point Problems

Authors: Zaslavski, Alexander J.

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  • 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
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  • ISBN 978-3-319-33255-0
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Hardcover $139.99
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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 title says it all: this book is a compilation of studies of algorithms for computing approximate solutions to the problem of finding common fixed points of several operators in the presence of computational errors. … The perspective on the analysis of algorithms with fixed computational error is new, and the book is a tutorial on how to execute this analysis for dynamical string-averaging methods, which includes many classical algorithms as special cases.” (Russell Luke, Mathematical Reviews, May, 2017)

“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)


Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-319-33255-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
Softcover $139.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Approximate Solutions of Common Fixed-Point Problems
Authors
Series Title
Springer Optimization and Its Applications
Series Volume
112
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-33255-0
DOI
10.1007/978-3-319-33255-0
Hardcover ISBN
978-3-319-33253-6
Softcover ISBN
978-3-319-81467-4
Series ISSN
1931-6828
Edition Number
1
Number of Pages
IX, 454
Topics