Alternating projections in CAT(0) spaces

Alternating projections in CAT(0) spaces

By using recently developed theory which extends the idea of weak convergence into CAT(0) space we prove the convergence of the alternating projection method for convex closed subsets of a CAT(0) space. Given the right notion of weak convergence it turns out that the generalization of the well-known...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 385; no. 2; pp. 599 - 607
Main Authors: Bačák, Miroslav, Searston, Ian, Sims, Brailey
Format: Journal Article
Language:English
Published: Elsevier Inc 15-01-2012
Subjects:
Algorithm
Alternating projections
CAT space
Convex optimization
Feasibility problem
Nearest point mapping
Non-expansive mapping
Non-positive curvature
Weak convergence
Alternating projections
Weak convergence
Convex optimization
CAT space
Nearest point mapping
Non-expansive mapping
Feasibility problem
Algorithm
Non-positive curvature
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Summary:By using recently developed theory which extends the idea of weak convergence into CAT(0) space we prove the convergence of the alternating projection method for convex closed subsets of a CAT(0) space. Given the right notion of weak convergence it turns out that the generalization of the well-known results in Hilbert spaces is straightforward and allows the use of the method in a nonlinear setting. As an application, we use the alternating projection method to minimize convex functionals on a CAT(0) space.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.06.079