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Extensions of Convex Functions with Prescribed Subdifferentials by Azagra, Daniel; Ferrera, Juan; Gómez-Gil, Javier; Mudarra, Carlos is a scholarly article available to read on EtoBox.

What is Extensions of Convex Functions with Prescribed Subdifferentials about?

Let $E$ be an arbitrary subset of a Banach space $X$, $f: E \rightarrow \mathbb{R}$ be a function, and $G:E \rightrightarrows X^*$ be a set-valued mapping. We give necessary and sufficient conditions on $f, G$ for the existence of a continuous convex extension $F: X \rightarrow \mathbb{R} $ of $f$ such that the subdifferential $\partial F$ of $F$ coincides with $G$ on $E.$

Author

Azagra, Daniel; Ferrera, Juan; Gómez-Gil, Javier; Mudarra, Carlos

Published

2018

Language

EN