# Effective strong convergence of the proximal point algorithm in CAT(0) spaces

arXiv: https://arxiv.org/abs/1801.02179 · HTML: https://mlsanity.com/paper/1801.02179/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2018.

## Built on by (most cited first, 1 of 1)

- [Mean-square and sublinear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature](https://mlsanity.com/paper/2510.10697/) (2025)

## Abstract (arXiv)

We apply methods of proof mining to obtain uniform quantitative bounds on the strong convergence of the proximal point algorithm for finding minimizers of convex, lower semicontinuous proper functions in CAT(0) spaces. Thus, for uniformly convex functions we compute rates of convergence, while, for totally bounded CAT(0) spaces we apply methods introduced by Kohlenbach, the first author and Nicolae to compute rates of metastability.