Optimization on Solution Sets of Common Fixed Point Problems

1. Auflage 2021
ISBN: 978-3-030-78851-3
Verlag: Springer International Publishing

Buch, Englisch, Band 178, 434 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 674 g

Reihe: Springer Optimization 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.

Zielgruppe

Research

Autoren/Hrsg.

Zaslavski, Alexander J.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik Mathematik Operations Research

Inhaltsverzeichnis

Preface.- Introduction.- Fixed Point Subgradient Algorithm.- Proximal Point Subgradient Algorithm.- Cimmino Subgradient Projection Algorithm.- Iterative Subgradient Projection Algorithm.- Dynamic Strong-Averaging Subgradient Algorithm.- Fixed Point Gradient Projection Algorithm.- Cimmino Gradient Projection Algorithm.- A Class of Nonsmooth Convex Optimization Problems.- Zero-Sum Games with Two Players.- References.- Index.

Über Autor(innen)

Alexander J. Zaslavski is professor in the Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel. He has authored numerous books with Springer, the most recent of which include Turnpike Theory for the Robinson–Solow–Srinivasan Model (978-3-030-60306-9),  The Projected Subgradient Algorithm in Convex Optimization (978-3-030-60299-4),  Convex Optimization with Computational Errors (978-3-030-37821-9), Turnpike Conditions in Infinite Dimensional Optimal Control (978-3-030-20177-7).