Summary

In the sequel, LaTeX is assumed.

Preliminary questions

1. Should a thin space separate “arg” from “min”?

This is a matter of personal preference. The default definition for limsup has a thin space, on the other hand “arcsin” is usually written without a space between the two components. Consistency is, as always, the keyword: using a macro definition will ensure it and also easiness in modifying the typesetting in the whole document, if switching from one option to another is needed.

2. Should limits go below the operator in display style?

Also this is debatable and conventions used in the field the document is written for should be followed.

3. Should the operator name be typeset upright?

Definitely, like all other operator/function names such as sine and cosine.

Available tools

1. amsmath

With amsmath one can do, in the preamble,

DeclareMathOperator*{argmin}{arg,min} % thin space, limits underneath in displays

DeclareMathOperator*{argmin}{argmin} % no space, limits underneath in displays

DeclareMathOperator{argmin}{arg,min} % thin space, limits on side in displays

DeclareMathOperator{argmin}{argmin} % no space, limits on side in displays

Of course, only one of these should be used. In the document it's sufficient to type argmin and the spacing around the operator will be the right one according to the common rules of math typesetting.

The seemingly different

newcommand{argmin}{operatornamewithlimits{argmin}}

is not really so, because it's essentially the same as DeclareMathOperator*{argmin}{argmin}; moreover it uses a deprecated command, that should be operatorname*.

2. No package

The following definitions are very similar to the ones above, in the same order

newcommand{argmin}{mathop{mathrm{arg,min}}

newcommand{argmin}{mathop{mathrm{argmin}}

newcommand{argmin}{mathop{mathrm{arg,min}nolimits}

newcommand{argmin}{mathop{mathrm{argmin}nolimits}

With underset

underset{x}{mathrm{argmin}}

This also was mentioned in the question and in one answer, but it is wrong, as the visual comparison will show.

3. Differences

The “no package” version is much more rigid than the amsmath version, because this package can receive the nonamelimits option that will automatically change all operators such as lim, max that usually have limits underneath (in displays) to have them on the side. The same option would of course act also on newly defined operators, provided DeclareMathOperator* has been used.

Test document

In the following test document, the proposed definitions or constructions will be compared.

documentclass{article}

usepackage{amsmath}



% limits underneath

DeclareMathOperator*{argminA}{arg,min} % Jan Hlavacek

DeclareMathOperator*{argminB}{argmin}   % Jan Hlavacek

DeclareMathOperator*{argminC}{argmin}   % rbp



newcommand{argminD}{arg!min} % AlfC



newcommand{argminE}{mathop{mathrm{argmin}}}          % ASdeL

newcommand{argminF}{mathop{mathrm{argmin}}limits}   % ASdeL



% limits on side

DeclareMathOperator{argminG}{arg,min} % Jan Hlavacek

DeclareMathOperator{argminH}{argmin}   % Jan Hlavacek

newcommand{argminI}{mathop{mathrm{argmin}}nolimits} % ASdeL



newcommand{cs}[1]{texttt{symbol{`\}#1}}



begin{document}



begin{align}

&cs{argminA}  & argminA_x f(x) &= {x mid f(x) = min_{x'} f(x')} \

&cs{argminB}  & argminB_x f(x) &= {x mid f(x) = min_{x'} f(x')} \

&cs{argminC}  & argminC_x f(x) &= {x mid f(x) = min_{x'} f(x')} \

&cs{argminD}  & argminD_x f(x) &= {x mid f(x) = min_{x'} f(x')} \

&cs{argminE}  & argminE_x f(x) &= {x mid f(x) = min_{x'} f(x')} \

&cs{argminF}  & argminF_x f(x) &= {x mid f(x) = min_{x'} f(x')} \

&cs{underset} & underset{x}{mathrm{argmin}} f(x) &= {x mid f(x) = min_{x'} f(x')}\

&cs{argminG}  & argminG_x f(x) &= {x mid f(x) = min_{x'} f(x')} \

&cs{argminH}  & argminH_x f(x) &= {x mid f(x) = min_{x'} f(x')} \

&cs{argminI}  & argminI_x f(x) &= {x mid f(x) = min_{x'} f(x')}

end{align}



end{document}

Results

As predicted, many lines typeset the same. However, the macros defined with mathop will not obey the nonamelimits option. Also the result of argminD is clearly wrong, as the limit is typeset below “max” and not below the whole operator name.

The construction with underset is wrong because it will not use the correct spacing after the operator: a thin space follows all others and it is the right way to typeset. Compare sin x and mathrm{sin}x to see this thin space in a different context.

Note that argminC and argminA give the same result, as well as argminD and argminB. Explanation: arg and max are already defined as operators, so TeX inserts a thin space if one directly follows another one. Using argminC or argminD just makes TeX spin its wheels a little more, with no advantage over argminA or argminB.

I use newcommand{argmin}{operatornamewithlimits{argmin}}.

Use usepackage{amsmath} and then:

operatorname*{argmin}_theta f(x)

Or similarly (for adding a space),

operatorname*{arg,max}_theta f(x)

Just another alternative (in some sense the poorer solution around, see comment below), could be to define argmin in terms of min and arg commands.

newcommand{argmin}{arg!min}

In this way, 1) argmin will behave always the same way as min, 2) doesn't need amsmath or care about operator... commands 3) yes, the variable in not centered (it is centered in the min part), but that may even be what you want (since it is centered in the same ways a min, also the 'g' in arg doesn't further lower the under-argument).

documentclass[fleqn]{article}

newcommand{argmin}{arg!min}

begin{document}



[ argmin_x f(x) = {x | f(x) = min_{x'} f(x')} ]

[ min_x f(x) = {f(x) | f(x) < f(x_0) forall x_0 in R ]



end{document}

or you could use the underset command. For example:

    R = underset{n} {mathrm{argmax}} ~P(L_n|mathbf{x})

I would use mathop and mathrm, and eventually limits or nolimits, depending on the desired behavior when combined with _ and ^. See below.

documentclass{article}



begin{document}



{

nothing:

newcommand{argmin}{mathop{mathrm{argmin}}}

$argmin_a^b$

$$argmin_a^b$$

}



{

limits:

newcommand{argmin}{mathop{mathrm{argmin}}limits}

$argmin_a^b$

$$argmin_a^b$$

}



{

nolimits:

newcommand{argmin}{mathop{mathrm{argmin}}nolimits}

$argmin_a^b$

$$argmin_a^b$$

}



end{document}

This works without any additional package. However it will create a new line.

$$pi(s) = argmax_theta$$