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MiS Preprint
51/2011

Alternating projections CAT(0) spaces

Miroslav Bačák, Ian Searston and Brailey Sims

Abstract

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.

Received:
Aug 15, 2011
Published:
Aug 16, 2011
MSC Codes:
46C50, 53C23, 47H09, 49J27
Keywords:
Nonpositive curvature, alternating projections, weak convergence

Related publications

inJournal
2012 Repository Open Access
Miroslav Bačák, Ian Searston and Brailey Sims

Alternating projections in CAT(0) spaces

In: Journal of mathematical analysis and applications, 385 (2012) 2, pp. 599-607