The proximal point algorithm in metric spaces
Optimization and Control
2012-07-02 v1 Metric Geometry
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 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.
Cite
@article{arxiv.1206.7074,
title = {The proximal point algorithm in metric spaces},
author = {Miroslav Bacak},
journal= {arXiv preprint arXiv:1206.7074},
year = {2012}
}
Comments
This paper was accepted to Israel journal of mathematics. The final version may differ