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Algorithms for Solving Common Fixed Point Problems

  • Alexander J.┬áZaslavski

Part of the Springer Optimization and Its Applications book series (SOIA, volume 132)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Alexander J. Zaslavski
    Pages 1-18
  3. Alexander J. Zaslavski
    Pages 19-67
  4. Alexander J. Zaslavski
    Pages 69-144
  5. Alexander J. Zaslavski
    Pages 145-176
  6. Alexander J. Zaslavski
    Pages 177-235
  7. Alexander J. Zaslavski
    Pages 237-253
  8. Alexander J. Zaslavski
    Pages 255-279
  9. Alexander J. Zaslavski
    Pages 281-306
  10. Back Matter
    Pages 307-316

About this book

Introduction

This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. Convex feasibility problems search for a common point of a finite collection of subsets in a Hilbert space; common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space. A variety of algorithms are considered in this book for solving both types of problems,  the study of which has fueled a rapidly growing area of research. This monograph is timely and highlights the numerous applications to engineering, computed tomography, and radiation therapy planning.

Totaling eight chapters, this book begins with an introduction to foundational material and moves on to examine iterative methods in metric spaces. The dynamic string-averaging methods for common fixed point problems in normed space are analyzed in Chapter 3. Dynamic string methods, for common fixed point problems in a metric space are introduced and discussed in Chapter 4. Chapter 5 is devoted to the convergence of an abstract version of the algorithm which has been called  component-averaged row projections (CARP). Chapter 6 studies a proximal algorithm for finding a common zero of a family of maximal monotone operators. Chapter 7 extends the results of Chapter 6 for a dynamic string-averaging version of the proximal algorithm. In Chapters 8 subgradient projections algorithms for convex feasibility problems are examined for infinite dimensional Hilbert spaces. 

Keywords

fixed point problems Hilbert space convex feasibility problems tomography Dynamic string methods

Authors and affiliations

  • Alexander J.┬áZaslavski
    • 1
  1. 1.Department of MathematicsTechnion:Israel Institute of TechnologyHaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-77437-4
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-77436-7
  • Online ISBN 978-3-319-77437-4
  • Series Print ISSN 1931-6828
  • Series Online ISSN 1931-6836
  • Buy this book on publisher's site