Definition [lcc-002M]

Let X be a convex space. A convex function on X is a function f: X \to \mathbb {R} so that f(\theta x + (1-\theta )x') \leq \theta f(x) + (1-\theta )f(x')

A concave function is a function so that -f is convex (in other words, f satisfies the opposite inequality).