Geometric properties of maximal monotone operators and convex functions which may represent them

TL;DR

This paper explores the geometric characteristics of maximal monotone operators and their convex function representations, analyzing conditions for bounded range and providing examples of non-type (D) operators.

Contribution

It establishes new links between geometric properties of maximal monotone operators and their convex function representations, including conditions for bounded range and examples of non-type (D) operators.

Findings

Identifies geometric conditions for convex functions to represent maximal monotone operators.

Provides criteria for bounded range in convex representations.

Constructs an example of a non type (D) operator within this framework.

Abstract

We study the relations between some geometric properties of maximal monotone operators and generic geometric and analytical properties of the functions on the associate Fitzpatrick family of convex representations. We also investigate under which conditions a convex function represents a maximal monotone operator with bounded range and provide an example of a non type (D) operator on this class.