Linear Convergence of Generalized Proximal Point Algorithms for Monotone Inclusion Problems

TL;DR

This paper establishes conditions under which generalized proximal point algorithms achieve linear convergence when solving monotone inclusion problems, expanding theoretical understanding of their efficiency.

Contribution

It provides new linear convergence results for generalized proximal point algorithms under metric subregularity or Lipschitz inverse assumptions.

Findings

Q-linear convergence under metric subregularity

R-linear convergence with Lipschitz inverse

Comparison with existing convergence results

Abstract

We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is metrically subregular or that the inverse of the monotone operator is Lipschitz continuous, we provide Q-linear and R-linear convergence results on generalized proximal point algorithms. Comparisons between our results and related ones in the literature are presented in remarks of this work.