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Obviously, $f(x)$ is called the "maximum value" or simply "maximum", but what is $x$ called? The maximizer?

Additionally, what if $f(x)$ is minimum or simply an extremum?

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    $\begingroup$ "maximizer" sounds fine to me. $\endgroup$ – David Mitra Oct 11 '13 at 22:04
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    $\begingroup$ The Maximizer strikes again... $\endgroup$ – copper.hat Oct 11 '13 at 22:31
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    $\begingroup$ Sometimes known as the $\arg \max$, albeit this is usually the set of parameters that attain the maximum. $\endgroup$ – copper.hat Oct 11 '13 at 22:32
  • $\begingroup$ "Parameter that attains the maximum" is also a good term for the case that learning potentially new terminology is not the scope of a paper. $\endgroup$ – Vortico Oct 12 '13 at 2:45
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It's often called the 'arg max' ('argument maximum'; similarly 'arg min'):

http://en.wikipedia.org/wiki/Arg_max

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    $\begingroup$ Thanks. This seems well accepted enough. $\endgroup$ – Vortico Oct 11 '13 at 22:08
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    $\begingroup$ Technically, arg max is the set of maximizers. This is true even if the maximizer $x^*$ is unique, that is, if $f(x^*)>f(x)$ for any $x\neq x^*$ in the domain of $f$. In this case, you could call $x^*$ the maximizer and $\{x^*\}$ the arg max. Despite the abuse of terminology, however, $x^*$ is often simply called the arg max anyway. $\endgroup$ – triple_sec Oct 11 '13 at 23:52

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