Alternating projections in CAT(0) spaces

Title: Alternating projections in CAT(0) spaces
Creator: Bačák, Miroslav; Searston, Ian; Sims, Brailey
Relation: Journal of Mathematical Analysis and Applications Vol. 385, Issue 2, p. 599-607
Publisher Link: http://dx.doi.org/10.1016/j.jmaa.2011.06.079
Publisher: Academic Press
Resource Type: journal article
Date: 2012
Description: 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.
Subject: non-positive curvature; CAT(0) space; alternating projections; feasibility problem; nearest point mapping; non-expansive mapping; weak convergence; convex optimization; algorithm
Identifier: http://hdl.handle.net/1959.13/1057172
Identifier: uon:16145
Identifier: ISSN:0022-247X
Language: eng
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