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