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The composition of projections onto closed convex sets in Hilbert space is asymptotically regular
Author(s):
Heinz
H.
Bauschke
Journal:
Proc. Amer. Math. Soc.
131
(2003),
141-146.
MSC (2000):
Primary 47H05, 47H09, 90C25
Posted:
May 9, 2002
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Abstract:
The composition of finitely many projections onto closed convex sets in Hilbert space arises naturally in the area of projection algorithms. We show that this composition is asymptotically regular, thus proving the so-called ``zero displacement conjecture'' of Bauschke, Borwein and Lewis. The proof relies on a rich mix of results from monotone operator theory, fixed point theory, and convex analysis.
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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
DOI:
10.1090/S0002-9939-02-06528-0
PII:
S 0002-9939(02)06528-0
Received by editor(s):
February 20, 2001
Received by editor(s) in revised form:
August 13, 2001
Posted:
May 9, 2002
Additional Notes:
The author's research was supported by NSERC
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2002,
American Mathematical Society
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