Explicit Convergence Rate of The Proximal Point Algorithm under R-Continuity

TL;DR

This paper investigates the convergence rate of the Proximal Point Algorithm under R-continuity, highlighting its advantages over other regularity conditions in optimization convergence analysis.

Contribution

It introduces explicit convergence rate results for PPA assuming R-continuity, expanding understanding of convergence behavior under this condition.

Findings

R-continuity offers advantages in convergence analysis.

Explicit convergence rates for PPA under R-continuity are derived.

Properties of R-continuity are characterized.

Abstract

The paper provides a thorough comparison between R-continuity and other fundamental tools in optimization such as metric regularity, metric subregularity and calmness. We show that R-continuity has some advantages in the convergence rate analysis of algorithms solving optimization problems. We also present some properties of R-continuity and study the explicit convergence rate of the Proximal Point Algorithm (PPA) under the R-continuity.