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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 (www.arxiv.org) 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
82/2011

Proximal Point Algorithm in Metric Spaces

Miroslav Bačák

Abstract

The proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of non-positive curvature. We prove that the sequence generated by the proximal point algorithm weakly converges to a minimizer, and also discuss a related question: convergence of the gradient flow.

Received:
Dec 9, 2011
Published:
Dec 9, 2011
Keywords:
proximal point algorithm, gradient flow semigroup, Nonpositive curvature

Related publications

inJournal
2013 Repository Open Access
Miroslav Bačák

The proximal point algorithm in metric spaces

In: Israel journal of mathematics, 194 (2013) 2, pp. 689-701