Algorithms For Solving Common Fixed Point Problems - Zaslavski Alexander J. | Libro Springer 01/2019 - HOEPLI.it


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zaslavski alexander j. - algorithms for solving common fixed point problems

Algorithms for Solving Common Fixed Point Problems




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 01/2019
Edizione: Softcover reprint of the original 1st ed. 2018





Sommario

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.







Trama

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. 








Altre Informazioni

ISBN:

9783030084554

Condizione: Nuovo
Collana: Springer Optimization and Its Applications
Dimensioni: 235 x 155 mm Ø 498 gr
Formato: Brossura
Pagine Arabe: 316
Pagine Romane: viii






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