On Projection Algorithms for Solving Convex Feasibility Problems

Abstract. Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given. Key words. angle between two subspaces, averaged mapping, Cimmino’s method, computerized tomography, convex feasibility problem, convex function, convex inequalities, convex programming, convex set, Fejér monotone