Let $U \subseteq \mathbb{R}^D$ be a D5007: Standard open euclidean real set such that
| (i) | $f : U \to \mathbb{R}$ is a D5614: Differentiable real function on $U$ |
Then the following statements are equivalent
| (1) | $f$ is a D5606: Subconvex real function |
| (2) | \begin{equation} \forall \, x, y \in U : f(y) \geq f(x) + \nabla f(x)^T (y - x) \end{equation} |