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 $S$,

$$\arg \underset{x\in S}{\min }f(x)=\{x\in S:f(x)=\underset{y\in S}{\min }f(y)\}.$$

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

$$\arg \underset{x\in S}{\max }f(x)=\{x\in S:f(x)=\underset{y\in S}{\max }f(y)\}.$$

Title	arg min and arg max
Canonical name	ArgMinAndArgMax
Date of creation	2013-03-22 14:27:55
Last modified on	2013-03-22 14:27:55
Owner	kshum (5987)
Last modified by	kshum (5987)
Numerical id	11
Author	kshum (5987)
Entry type	Definition
Classification	msc 00A05
Defines	argmin argmax