Editing Arg max (section)

=== Arg min<!--'Arg min' redirects here--> ===
The notion of <math>\operatorname{argmin}</math> (or <math>\operatorname{arg\,min}</math>), which stands for '''argument of the minimum''', is defined analogously. For instance,

:<math>\underset{x \in S}{\operatorname{arg\,min}} \, f(x) := \{ x \in S ~:~ f(s) \geq f(x)  \text{ for all } s \in S \}</math>

are points <math>x</math> for which <math>f(x)</math> attains its smallest value. It is the complementary operator of {{nowrap|<math>\operatorname{arg\,max}</math>.}}

In the special case where <math>Y = [-\infty,\infty] = \R \cup \{ \pm\infty \}</math> are the [[extended real numbers]], if <math>f</math> is identically equal to <math>-\infty</math> on <math>S</math> then <math>\operatorname{argmin}_S f := \varnothing</math> (that is, <math>\operatorname{argmin}_S -\infty := \varnothing</math>) and otherwise <math>\operatorname{argmin}_S f</math> is defined as above and moreover, in this case (of <math>f</math> not identically equal to <math>-\infty</math>) it also satisfies:
:<math>\operatorname{argmin}_S f := \left\{ x \in S ~:~ f(x) = \inf {}_S f \right\}.</math>{{sfn|Rockafellar|Wets|2009|pp=1-37|ignore-err=yes}}