# Convex function

Jump to: navigation, search

Let $LaTeX: f:X\rightarrow R$. Then $LaTeX: f$ is convex if $LaTeX: X$ is a convex set, and for $LaTeX: x, y \in X$ and $LaTeX: 0 \le a \le 1$:

$LaTeX: f(ax + (1-a)y) \le af(x) + (1-a)f(y)$.

Equivalently, its epigraph is convex.