Extensions of convex functions with prescribed subdifferentials
| Autor: | Azagra, Daniel, Ferrera, Juan, Gómez-Gil, Javier, Mudarra, Carlos |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $E.$ Comment: In this new version we added several examples in the introduction to illustrate the role of our conditions in an infinite-dimensional setting |
| Databáze: | arXiv |
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