Calculus Rules for Proximal ε-Subdifferentials and Inexact Proximity Operators of Weakly Convex Functions

This work investigates proximal ε-subdifferentials and derives sum rules for weakly convex functions, incorporating the corresponding moduli of weak convexity. It also analyzes inexact proximity operators for weakly convex functions in terms of proximal ε-subdifferentials and the related notion of criticality.