On projection algorithms for solving convex feasibility problems. (English) Zbl 0865.47039

Bauschke, Heinz H.; Borwein, Jonathan M.

SIAM Rev. 38, No. 3, 367-426 (1996).

Summary: 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 in questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.

MSC:

47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
90C25	Convex programming
65J10	Numerical solutions to equations with linear operators
92C55	Biomedical imaging and signal processing

Keywords:

angle between two subspaces; averaged mapping; Cimmino’s method; convex inequalities; convex programming; convex set; Fejér monotone sequence; firmly nonexpansive mapping; image recovery; Kaczmarz’s method; nonexpansive mapping; orthogonal projection; Slater point; subdifferential; subgradient algorithm; successive projections; computerized tomography; convex feasibility problems; quality of convergence