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arXiv · 1811.05538

Extensions of convex functions with prescribed subdifferentials

Daniel Azagra·Juan Ferrera·Javier Gómez-Gil·Carlos Mudarra
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Abstract

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 $E.$

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Daniel Azagra, Juan Ferrera, Javier Gómez-Gil, Carlos Mudarra. 2018-11-13. Extensions of convex functions with prescribed subdifferentials. https://arxiv.org/abs/1811.05538

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