# Frank-Wolfe Theorem

If a quadratic function is bounded from below on a nonempty polyhedron, it attains a minimum there. In mathematical notation, we are given that $LaTeX: X$ is a nonempty polyhedron. Then, if there exists $LaTeX: L$ such that $LaTeX: f(x) \ge L$ for all $LaTeX: x \in X$, there exists $LaTeX: x^* \in X$ such that $LaTeX: f(x^*) \le f(x)$ for all $LaTeX: x \in X$.