The composition of projections onto closed convex sets in Hilbert space is asymptotically regular
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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.References
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Additional Information
- Heinz H. Bauschke
- Affiliation: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1
- MR Author ID: 334652
- Email: hbauschk@uoguelph.ca
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 141-146
- MSC (2000): Primary 47H05, 47H09, 90C25
- DOI: https://doi.org/10.1090/S0002-9939-02-06528-0
- MathSciNet review: 1929033