Proximal Point Algorithm in Metric Spaces

Miroslav Bačák

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Submission date: 09. Dec. 2011
published in: Israel journal of mathematics, 194 (2013) 2, p. 689-701 
DOI number (of the published article): 10.1007/s11856-012-0091-3
Bibtex
with the following different title: The proximal point algorithm in metric spaces
Keywords and phrases: proximal point algorithm, gradient flow semigroup, Nonpositive curvature

Abstract:
The proximal point algorithm, which is a well-known tool for finding min- ima 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.