Introduction

Abstract

AbstractIn Chap. 1 we present the notation, definitions and basic facts about convex subsets and convex functions defined on a Hilbert space, convergence and differentiation properties, the properties of matrices, etc., which will be used in further parts of the book. Then we define the metric projection for a Hilbert space and present its basic properties. This operator plays an important role in further parts of the book. Finally, we present several convex optimization problems: convex minimization, variational inequalities, convex feasibility problems and split feasibility problems. These problems as well as the methods for solving them have applications in various areas of mathematics. Furthermore, these abstract problems can be treated as mathematical models for many practical problems which arise in physical, medical, technical and information sciences.KeywordsSplit Feasibility Problem (SFP)Convex Feasibility Problem (CFP)Proximity FunctionLinear Feasibility Problem (LFP)Common Fixed Point Problem (CFPP)These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.