I'm reading a text by rockafellar and wets and in it, it defines the so called proper and improper function
What could be a concrete example of a function that is not proper? I failed to think up one.
2026-04-06 04:35:36.1775450136
What would be an example of an improper function?
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Hint: For every proper convex function $f$ on $\mathbb{R}^n$, there exists some $b \in \mathbb{R}^n$ and $\beta \in \mathbb{R}$ such that $f(x) \geq x \cdot b - \beta$ for every x.