Two modified proximal point algorithms in geodesic spaces with curvature bounded above

TL;DR

This paper develops and analyzes two modified proximal point algorithms for convex functions in complete geodesic spaces with curvature constraints, establishing their existence and convergence properties.

Contribution

It introduces two variants of the proximal point algorithm tailored for geodesic spaces with curvature bounds, extending convergence theory beyond Euclidean settings.

Findings

Proved existence of solutions for the algorithms.

Established convergence theorems in curved geodesic spaces.

Extended proximal point methods to non-Euclidean geometries.

Abstract

We obtain existence and convergence theorems on two variants of the proximal point algorithm for proper lower semicontinuous convex functions in complete geodesic spaces with curvature bounded above.