What would be an example of an improper function?

Question

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.

See http://math.stackexchange.com/questions/1105842/improper-convex-function for an example. (One that's convex, even.) — Misha Lavrov, Mar 26 '17 at 17:57

score 1 · Accepted Answer · answered Mar 26 '17 at 18:06

1

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.

answered Mar 26 '17 at 18:06

awright96

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What would be an example of an improper function?

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