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:
https://doi.org/10.1090/S0002-9939-02-06528-0

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