# Concave function

The real valued function $LaTeX: f$ is concave if its domain, say $LaTeX: X$, is a convex set, and for $LaTeX: x, y \in X$ and $LaTeX: 0 \le a \le 1$:
$LaTeX: f(ax + (1-a)y) \ge af(x) + (1-a)f(y).$
Equivalently, $LaTeX: f$ is concave if its hypograph is a convex set or if its negative is a convex function.