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Local Search
Suppose we are given some optimization problem
\[ \begin{aligned} &\min & f(\mathbf x)\\ &\text{subject to}& \mathbf x &\in S \end{aligned} \]where \( S \subset \mathbb R^n \) and \( f \colon S \to \R \) . The idea of local search is as follows: for every \( \mathbf x \in S \) , define \( N_{\mathbf x} \) to be the neighborhood of \( \mathbf x \) .