The proximal point method and its two variants for monotone vector fields in Hadamard spaces

TL;DR

This paper establishes the existence and convergence of sequences generated by the proximal point method and its variants for monotone vector fields in Hadamard spaces, supported by foundational property analysis.

Contribution

It introduces new convergence results for proximal point methods in Hadamard spaces and explores fundamental properties of tangent spaces and resolvents.

Findings

Proves convergence of proximal point sequences in Hadamard spaces.

Analyzes properties of tangent spaces and resolvents in these spaces.

Establishes foundational results for monotone vector fields.

Abstract

We prove existence and convergence of sequences generated by the proximal point method and its two variants for monotone vector fields in Hadamard spaces. Before obtaining our results, we investigate some fundamental properties of tangent spaces, resolvents, and monotone vector fields in such spaces.