# Fritz John conditions

Suppose $LaTeX: x^*$ is in $LaTeX: \arg\!\max\{f(x): x \in \mathbb{R}^n, \; g(x) \le 0\}$, where $LaTeX: f$ and $LaTeX: g$ are in smooth. Then, there exists multipliers $LaTeX: (y_0, y) \ge 0$, not all zero, such that
$LaTeX: y_0 \nabla f(x) - y^T \nabla g(x) = 0 \mbox{ and } y^Tg(x) = 0.$