Marginable functions on Fr\'echet spaces

TL;DR

This paper extends the theory of shadow variables from monotone operators to demonstrate that properties of lower semicontinuous convex functions also hold for a broader class called marginable convex functions.

Contribution

It introduces the concept of marginable convex functions and proves that results known for lower semicontinuous convex functions apply to this larger class.

Findings

Results for lower semicontinuous convex functions are valid for marginable convex functions.

Uses shadow variables technique to establish these generalizations.

Broadens the applicability of convex analysis techniques.

Abstract

This paper is about the technique of {\em shadow variables} that was used in the theory of monotone operators. In this paper, we use it to show that certain results that were originally proved for lower semicontinuous convex functions are in fact true for {\em marginable} convex functions.