Calculus rules for proximal ε-subdifferentials and inexact proximity operators for weakly convex functions

We investigate proximal ε-subdifferentials and derive sum rules that hold for weakly convex function, by incorporating the corresponding moduli of weak convexity into the respective formulas. As an application, we analyse inexact proximity operators for weakly convex functions in terms of proximal ε-subdifferentials and the related notion of criticality.