Algorithms for Solving Common Fixed Point Problems

Inhaltsverzeichnis

1. Introduction.- 2. Iterative methods in metric spaces.- 3. Dynamic string-averaging methods in normed spaces.- 4. Dynamic string-maximum methods in metric spaces.- 5. Abstract version of CARP algorithm.- 6. Proximal point algorithm.- 7. Dynamic string-averaging proximal point algorithm.- 8. Convex feasibility problems.




Springer Optimization and Its Applications Band 132

Algorithms for Solving Common Fixed Point Problems

Buch (Gebundene Ausgabe, Englisch)

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Beschreibung

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. 

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

14.05.2018

Verlag

Springer

Seitenzahl

316

Maße (L/B/H)

24,1/15,6/2,5 cm

Beschreibung

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

14.05.2018

Verlag

Springer

Seitenzahl

316

Maße (L/B/H)

24,1/15,6/2,5 cm

Gewicht

642 g

Auflage

1st ed. 2018

Sprache

Englisch

ISBN

978-3-319-77436-7

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  • Algorithms for Solving Common Fixed Point Problems
  • 1. Introduction.- 2. Iterative methods in metric spaces.- 3. Dynamic string-averaging methods in normed spaces.- 4. Dynamic string-maximum methods in metric spaces.- 5. Abstract version of CARP algorithm.- 6. Proximal point algorithm.- 7. Dynamic string-averaging proximal point algorithm.- 8. Convex feasibility problems.