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Theorem : Lagrange's Theorem

Let $\b{x}^* $ be a local extremizer of $ f: \R^n \to \R $, subject to $\b{h}(\b{x}) = \b{0}, \b{h} : \R^n \to \R^m, m \leq n $. Assume that $\b{x}^* $ is a regular point. Then there exists $\b{\lambda}^* \in \R^m$ such that

$$ Df(\b{x}^*) + \transpose{ \b{\lambda}^* } D \b{h}(\b{x}^*) = \transpose{ \b{0}} $$