English

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.

Keywords

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

R2 v1 2026-06-21T21:28:14.759Z