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

We investigate inexact proximity operators for weakly convex functions. To this aim, we derive sum rules for proximal ϵ-subdifferentials, by incorporating the moduli of weak convexity of the functions into the respective formulas. This allows us to investigate inexact proximity operators for weakly convex functions in terms of proximal ϵ-subdifferentials.