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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new proximal point iteration that converges weakly but not in norm


Authors: H. H. Bauschke, J. V. Burke, F. R. Deutsch, H. S. Hundal and J. D. Vanderwerff
Journal: Proc. Amer. Math. Soc. 133 (2005), 1829-1835
MSC (2000): Primary 65K10, 90C25; Secondary 47H05, 47H09, 65K05
Published electronically: January 25, 2005
MathSciNet review: 2120284
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Abstract: In 1991, Güler constructed a proximal point iteration that converges weakly but not in norm. By building on a recent result of Hundal, we present a new, considerably simpler, example of this type.


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Additional Information

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

J. V. Burke
Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
Email: burke@math.washington.edu

F. R. Deutsch
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: deutsch@math.psu.edu

H. S. Hundal
Affiliation: Momentum Investment Services, 146 Cedar Ridge Drive, Port Matilda, Pennsylvania 16870
Email: hundal@math.psu.edu

J. D. Vanderwerff
Affiliation: Department of Mathematics, La Sierra University, Riverside, California 92515
Email: jvanderw@LaSierra.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07719-1
PII: S 0002-9939(05)07719-1
Keywords: Proximal point algorithm, weak convergence, support point.
Received by editor(s): September 13, 2002
Published electronically: January 25, 2005
Additional Notes: The first author was supported in part by the Natural Sciences and Engineering Research Council of Canada. The second author was supported in part by the National Science Foundation Grant DMS-0203175. The third author was supported in part by the National Science Foundation Grant DMS-0204569.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society