MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Alternating projections CAT(0) spaces

Miroslav Bačák, Ian Searston and Brailey Sims


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.

MSC Codes:
46C50, 53C23, 47H09, 49J27
Nonpositive curvature, alternating projections, weak convergence

Related publications

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