# 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 $S$,

 ${\arg\max}_{x\in S}f(x)=\{x\in S:\,f(x)=\max_{y\in S}f(y)\}.$
Title arg min and arg max ArgMinAndArgMax 2013-03-22 14:27:55 2013-03-22 14:27:55 kshum (5987) kshum (5987) 11 kshum (5987) Definition msc 00A05 argmin argmax