Alternating projections CAT(0) spaces
Miroslav Bačák, Ian Searston, and Brailey Sims
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Submission date: 15. Aug. 2011
published in: Journal of mathematical analysis and applications, 385 (2012) 2, p. 599-607
DOI number (of the published article): 10.1016/j.jmaa.2011.06.079
with the following different title: Alternating projections in CAT(0) spaces
MSC-Numbers: 46C50, 53C23, 47H09, 49J27
Keywords and phrases: Nonpositive curvature, alternating projections, weak convergence
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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.