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Construction of best Bregman approximations in reflexive Banach spaces


Authors: Heinz H. Bauschke and Patrick L. Combettes
Journal: Proc. Amer. Math. Soc. 131 (2003), 3757-3766
MSC (2000): Primary 41A65, 90C25; Secondary 41A29, 41A50
Published electronically: April 24, 2003
MathSciNet review: 1998183
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Abstract: An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space.


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Additional Information

Heinz H. Bauschke
Affiliation: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1
Email: hbauschk@uoguelph.ca

Patrick L. Combettes
Affiliation: Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie – Paris 6, 75005 Paris, France
Email: plc@math.jussieu.fr

DOI: https://doi.org/10.1090/S0002-9939-03-07050-3
Keywords: Best approximation, Bregman distance, decomposition, Haugazeau
Received by editor(s): June 28, 2002
Published electronically: April 24, 2003
Additional Notes: The first author was supported by the Natural Sciences and Engineering Research Council of Canada.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2003 American Mathematical Society