Calculus rules for proximal {\epsilon}-subdifferentials and inexact proximity operators for weakly convex functions

TL;DR

This paper develops sum rules for proximal epsilon-subdifferentials of weakly convex functions, enabling analysis of inexact proximity operators by incorporating weak convexity moduli.

Contribution

It introduces new calculus rules for proximal epsilon-subdifferentials of weakly convex functions, facilitating the study of inexact proximity operators.

Findings

Derived sum rules for proximal epsilon-subdifferentials incorporating weak convexity.

Provided a framework to analyze inexact proximity operators for weakly convex functions.

Enhanced understanding of calculus rules for weakly convex functions.

Abstract

We investigate inexact proximity operators for weakly convex functions. To this aim, we derive sum rules for proximal {\epsilon}-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 {\epsilon}-subdifferentials.