Optimization on Solution Sets of Common Fixed Point Problems

ISBN-13: 9783030788513 / Angielski / Miękka / 2022

Alexander J. Zaslavski

Opis

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.

Recenzje

"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)

Spis treści

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.

O autorze

​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).