%0 Journal Article
%T The proximal point algorithm in metric spaces
%A Miroslav Bacak
%J Mathematics
%D 2012
%I arXiv
%X 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 nonpositive 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.
%U http://arxiv.org/abs/1206.7074v1