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

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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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2005-06, Vol.133 (6), p.1829-1835
Main Authors: Bauschke, H. H., Burke, J. V., Deutsch, F. R., H. S. Hundal, Vanderwerff, J. D.
Format: Article
Language:English
Subjects:
Applied sciences
College mathematics
Exact sciences and technology
Hilbert spaces
Hyperplanes
Iterative methods
Mathematical analysis
Mathematical functions
Mathematical programming
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Operational research and scientific management
Operational research. Management science
Operator theory
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Perceptron convergence procedure
Sciences and techniques of general use
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Description
Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-05-07719-1