Fenchel subdifferential operators: a characterization without cyclic monotonicity

TL;DR

This paper introduces a new way to characterize Fenchel subdifferential operators that avoids cyclic monotonicity, simplifying understanding especially for sublinear functions and normal cone operators.

Contribution

It provides an alternative characterization of Fenchel subdifferential operators that does not rely on cyclic monotonicity, simplifying analysis for sublinear functions and normal cones.

Findings

New characterization of Fenchel subdifferential operators

Simplified analysis for sublinear functions

Simplified characterization of normal cone operators

Abstract

Fenchel subdifferential operators of lower semicontinuous proper convex functions on real Banach spaces are classically characterized as those operators that are maximally cyclically monotone or, equivalently, maximally monotone and cyclically monotone. This paper presents an alternative characterization, which does not involve cyclic monotonicity. In the case of subdifferential operators of sublinear functions, the new characterization substantially simplifies. Dually, the new characterization of normal cone operators is very simple, too.