Israel Journal of Mathematics

, Volume 194, Issue 2, pp 689–701

The proximal point algorithm in metric spaces


DOI: 10.1007/s11856-012-0091-3

Cite this article as:
Bačák, M. Isr. J. Math. (2013) 194: 689. doi:10.1007/s11856-012-0091-3


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.

Copyright information

© Hebrew University Magnes Press 2012

Authors and Affiliations

  1. 1.Max Planck InstituteLeipzigGermany