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

 

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


Author: Heinz H. Bauschke
Journal: Proc. Amer. Math. Soc. 131 (2003), 141-146
MSC (2000): Primary 47H05, 47H09, 90C25
Published electronically: May 9, 2002
MathSciNet review: 1929033
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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: http://dx.doi.org/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
Published electronically: May 9, 2002
Additional Notes: The author’s research was supported by NSERC
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society