3

I'm having some trouble regarding the layout of nested subscripts/superscripts when used as underscored argument of argmin/min/max operators.

I have defined \argmin{} operator as:

\DeclareMathOperator*{\argmin}{arg\,min}

and then used inside:

\[\bm \theta_c^p \coloneqq  \adjustlimits\argmin_{\bm \theta_c \in \mathbb{R}^{n_{p} } }  \max_{\bm \theta \in \mathcal{D}_{\bm \theta}} \left\| \bm \theta - \bm \theta_c \right\|_p \]

in order to get:

enter image description here

My issue is that the actual output is not completely satisfactory mainly owing to wrong size of the subscript 'p' of 'n': they are both scriptscriptstyle so they have the same size and it results in a quite odd layout. I have already tried manipulating the size with no success whatsoever, even with \scalebox.

Which could be a simple and clean solution to this problem?

EDIT: I removed the part of the question that makes it a duplicate, the rest of the question is completely different from the "height issue" of adjacent operators (thanks to the use of \adjustlimits it is not an issue anymore)

12
  • For the last problem, use _{\min} instead of _{min}. You also have a problem with the layout of \argmin (thin space between arg and min).
    – Bernard
    Dec 10, 2016 at 12:40
  • A simple solution would be \smash{...}, which makes the argument have no height. You could use this to eliminate the depth of the g and the height of the ^{n_p}. However, the formulas will be too close then. So instead you could do the opposite and add a \vphantom to the other part.
    – Scz
    Dec 10, 2016 at 12:50
  • Regarding the mark as duplicate, I fixed the question so that now it is a totally different subject. @egreg that works perfectly, it fixes the height issue, but not the size issue in the subscript of the superscript.
    – Vexx23
    Dec 10, 2016 at 14:10
  • @Bernard also this simple solution is perfect. As regards the thin space, I have followed the advices in tex.stackexchange.com/questions/5223/…
    – Vexx23
    Dec 10, 2016 at 14:10
  • @Scz it looks like I'm placing that command in the wrong way since it does not influence the layout
    – Vexx23
    Dec 10, 2016 at 14:10

2 Answers 2

1

You can get a smaller subscript with a trick:

\RequirePackage{fix-cm}
\documentclass{article}
\usepackage{mathtools,amssymb}
\usepackage{bm}

\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathSizes{5}{5}{4}{4}


\begin{document}

\[
\bm{\theta}_c^p \coloneqq
\adjustlimits\argmin_{\bm{\theta}_c \in \mathbb{R}^{n_{p}}}
             \max_{\bm{\theta} \in \mathcal{D}_{\bm \theta}}
             \lVert\bm{\theta} - \bm \theta_c \rVert_p
\]
\[
\bm{\theta}_c^p \coloneqq
\adjustlimits\argmin_{\bm{\theta}_c \in \mathbb{R}^{\text{$n_{p}$}}}
             \max_{\bm{\theta} \in \mathcal{D}_{\bm \theta}}
             \lVert\bm{\theta} - \bm \theta_c \rVert_p
\]

\end{document}

enter image description here

On the other hand, using a symbol with two different meanings in the same formula is not really recommended.

1
  • I think n_p is used because all the other letters, usually employed for integers, are used for different purposes (number of input p, number of outputs q, delay on the input m, delay on the output n, etc.) but yet you have made a very good point, this notation should be modified. Anyway the problem could arise also with consistent notations, so this solution will be useful anyway.
    – Vexx23
    Dec 11, 2016 at 9:22
4

Expanding on my comment, you should remember that you do not absolutely have to put the specification of the domain of \max or \min or ... as subscript to the word, but can use set notation instead, e.g.

\max \{ (x-3) : x \in [-1,1] \}

instead of `\max_{x\in [-1,1]} (x-3). This particularly appropriate when the domain specification is long and/or involves many levels of sub/superscripts. In you case, you could apply the technique to the outer argmin:

Sample output

\documentclass{article}

\usepackage{mathtools,amssymb,bm}

\DeclareMathOperator*{\argmin}{arg\,min}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}

\newcommand{\btheta}{\bm \theta}

\begin{document}

\begin{equation*}
  \btheta_c^p \coloneqq
  \argmin
  \Bigl\{
    \max_{\btheta \in \mathcal{D}_{\btheta}} \norm{\btheta - \btheta_c}_p
    : \btheta_c \in \mathbb{R}^{n_{p} }
  \Bigr\}
\end{equation*}

\end{document}
1
  • I didn't know this kind of notation yet, it is most useful, especially when writing very long constraints in the argument for linear programming or polynomial optimization problems
    – Vexx23
    Dec 11, 2016 at 10:48

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