Definition:Convex Real-Valued Function

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