Explicit convergence rate of the proximal point algorithm under R-continuity

This 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 for solving optimization problems. We also present some properties of R-continuity and study the explicit convergence rate of the proximal point algorithm $ (\mathbf{P}\mathbf{P}\mathbf{A}) $ under the R-continuity.