The composition of projections onto closed convex sets in Hilbert space is asymptotically regular

DOI10.1090/S0002-9939-02-06528-0zbMath1016.47038MaRDI QIDQ3151189

Heinz H. Bauschke

Publication date: 7 October 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

projectionsasymptotic regularityreal Hilbert spaceclosed convex setscomposition of projectionszero displacement conjecture

Mathematics Subject Classification ID

Convex programming (90C25) Monotone operators and generalizations (47H05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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Cites Work

• Convex functions, monotone operators and differentiability.
• Image d'une somme d'opérateurs monotones et applications
• Minimax monotonicity
• Maximal monotonicity of dense type, local maximal monotonicity, and monotonicity of the conjugate are all the same for continuous linear operators
• On Projection Algorithms for Solving Convex Feasibility Problems
• The solution by iteration of linear functional equations in Banach spaces
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