Optimization on Solution Sets of Common Fixed Point Problems

Beschreibung

This book is devoted to a detailed study of the subgradient projection method and its variants for convex optimization problems over the solution sets of common fixed point problems and convex feasibility problems. These optimization problems are investigated to determine good solutions obtained by different versions of the subgradient projection algorithm in the presence of sufficiently small computational errors.  The use of selected algorithms is highlighted including the Cimmino type subgradient, the iterative subgradient, and the dynamic string-averaging subgradient.  All results presented are new.  Optimization problems where the underlying constraints are the solution sets of other problems, frequently occur in applied mathematics. The reader should not miss the section in Chapter 1 which considers some examples arising in the real world applications. The problems discussed have an important impact in optimization theory as well. The book will be usefulfor researches interested in the optimization theory and its applications.
This book is devoted to a detailed study of the subgradient projection method and its variants for convex optimization problems over the solution sets of common fixed point problems and convex feasibility problems. These optimization problems are investigated to determine good solutions obtained by different versions of the subgradient projection algorithm in the presence of sufficiently small computational errors.  The use of selected algorithms is highlighted including the Cimmino type subgradient, the iterative subgradient, and the dynamic string-averaging subgradient.  All results presented are new.  Optimization problems where the underlying constraints are the solution sets of other problems, frequently occur in applied mathematics. The reader should not miss the section in Chapter 1 which considers some examples arising in the real world applications. The problems discussed have an important impact in optimization theory as well. The book will be useful for researches interested in the optimization theory and its applications.

Studies the influence of computational errors on minimization problems with a convex objective function on a common fixed point set of a finite family of quasi-nonexpansive mappings Highlights the use of Cimmino type subgradient algorithms Highlights the use of the iterative subgradient algorithms Highlights the use of the dynamic string-averaging subgradient algorithm

Autor*in

Alexander J. Zaslavski

Themen in »Optimization on Solution Sets of Common Fixed Point Problems«

subgradient algorithms quasi-nonexpansive mapping dynamioc string-averaging solution sets common fixed point problems Cimmino subgradient algorithm

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“Author … make accessible a number of topics that are not often found in many books. … All the algorithms are clearly explained and presented. The results presented in this book will be useful for problems with complicated sets of feasible points arising in engineering, computed tomography and radiation therapy planning. Overall, this book is an excellent contribution to the field of optimization, and it is highly recommended to the students and researchers interested in optimization theory and its applications.” (Samir Kumar Neogy, zbMATH 1479.49001, 2022)
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