Definition:Convex Real-Valued Function
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Definition
Real Vector Space
Let $\R^n$ be an $n$-dimensional real vector space.
Let $S \subseteq \R^n$ be a subset.
Let $f: S \to \overline \R$ be an extended real-valued function.
$f$ is convex if and only if its epigraph is a convex subset of $\R^{n+1}$.
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Also see
- Results about convex real-valued functions can be found here.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): convex function