All convex bodies are in the subdifferential of some everywhere differentiable locally Lipschitz function

Aris Daniilidis, Robert Deville, Sebastian Tapia-Garcia

We construct a differentiable locally Lipschitz function $f$ in ${\mathbb{R}}^N$ with the property that for every convex body $K\subset {\mathbb{R}}^N$ there exists $\bar x \in \math…