Frank-Wolfe Theorem

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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.

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