- 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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