Sane spacing after min max

Question

The default definitions of \min and \max insert basically no space after them, which looks really awful when stating optimisation problems, etc., in display equations. I could not figure out any way automatically insert space after them? The following, for one, did not work:

\renewcommand{\min}{\expandafter\,\operatorname*{min}}

The space still came before min. Is there a way that still causes super- and subscripts to be parsed correctly?

Addition: What I basically want is

\min_u\, G(u) + F(Ku)

in a display equation, without having to enter \, manually. A more complete statement, giving a better idea of the type of expressions, would be

\min_{u \in X}\, G(u)+F(Ku) \quad\text{subject to}\quad Au=b.

You really want that extra space there, but it would be nice not have to enter it manually.

Answer 1

The default definition of \min is

\def\min{\mathop{\operator@font min}}

so it is an operator like \log and will get a thin space in \min x but not in \min(x)

Your redefinition

\renewcommand{\min}{\expandafter\,\operatorname*{min}}

is the same as

\renewcommand{\min}{\,\operatorname*{min}}

and puts an additional thin space before the operator. the only effect of the \expandafter is to expand \operatorname one step before executing \, so your definition is actually equivalent to

\renewcommand{\min}{\,\protect\operatorname_*{min}}

where _ denotes a space character as one level of expansion just reveals the \protect that makes it a robust command.

Answer 2

As explained by egreg in his first comment, \min et. al. have the correct spacing when followed by a delimiter, because by intention, they operate on a set of values (over which to take the minimum). As you use it,

\min_u G(u) + F(Ku)

the expression is itself ambiguous, and the natural parsing as "minimum of G(u), plus...oh wait" causes some dissonance halfway through. So the real answer is not to do this, and write

\min_u \{ G(u) + F(Ku) \}

instead. As a bonus, you can drop the subscript and add some more lengthy conditions that would look bad in small print, like

\min_u \{ G(u) + F(Ku) \mid u \in X, Au = b \}

which has the advantage over your second snippet,

\min_{u \in X}\, G(u)+F(Ku) \quad\text{subject to}\quad Au=b

of not incorrectly making an external reference to the "bound variable" u outside its scope.

I realize that you may believe you are following some kind of convention in your field by omitting the delimiters. However, unless you have given the matter specific thought and developed a strong opinion, you should consider changing your style here, since it has both typographic issues (as you observed) as well as mathematical ones.

P.S. If you really must do it this way, probably the easiest workaround is to use an argument rather than a subscript. For instance,

\newcommand*\mymin[1][]{\min_{#1}\,}

See this minimal document comparing it with the "standard":

\documentclass{article}
\newcommand*\mymin[1][]{\min_{#1}\,}
\begin{document}
$\min A \quad \min_u A$

$\mymin A \quad \mymin[u] A$
\[ \min A \quad \min_u A\]
\[ \mymin A \quad \mymin[u] A\]
\end{document}

Why not use the subscript character directly? First, because parsing it is a pain, as it does not "collect" its argument conveniently as macros do, and therefore, it makes moving that argument difficult. And second, from a programming standpoint, there is only one thing you want to do with \min, which is subscript it, so it is more logical to associate it with an abstract "do this" operation. The abstraction has the nice side effect of enabling an abstract implementation, namely, to place a space afterwards.

Answer 3

Temporary solution. This one just checks if there is a subscript next to it. Nothing more.

\documentclass{scrartcl}
\usepackage{mathtools}
\makeatletter
\def\raremin{\@ifnextchar_\@rareminsub\@raremin}
\def\@rareminsub_#1{\min_{#1}\,}
\def\@raremin{\min\,}
\makeatother
\begin{document}
$ \raremin_u G(u) + F(Ku) $
\[ \raremin_u G(u) + F(Ku) \]
\end{document}