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# arg min and arg max

For a real-valued function $f$ with domain $S$, $\arg\min_{{x\in S}}f(x)$ is the set of elements in $S$ that achieve the global minimum in $S$,

${\arg\min}_{{x\in S}}f(x)=\{x\in S:\,f(x)=\min_{{y\in S}}f(y)\}.$ |

$\arg\max_{{x\in S}}f(x)$ is the set of elements in $S$ that achieve the global maximum in $S$,

${\arg\max}_{{x\in S}}f(x)=\{x\in S:\,f(x)=\max_{{y\in S}}f(y)\}.$ |

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