How to write a text below a math operator

Question

I want to achieve this

but if I use

\mathrm{argmax}_{y\in\mathcal{Y}}

it does not put y\in\mathcal{Y} below argmax. How can I solve this?

Answer 1

Welcome to TeX.SX! What you probably struggle with is the fact that TeX knows two different modes of typesetting math: inline and display. While display math is used to display mathematical formulas separate from floating text, inline math is used, well, in-line, that is, in the context of other surrounding text.

As for your concrete example, the argument {y \in \mathscr{Y}} will not be placed underneath "argmax" when you use inline math. This is a typographic decision made by TeX to reduce the space mathematical formulas take when typeset inline. If you use your command in an display-math environment, it will be typeset as you intend:

The above output is generated by the following code:

\documentclass{article}
\usepackage{amsmath}

\DeclareMathOperator*{\argmax}{argmax}

\begin{document}

This is inline: $\argmax_{y \in \mathcal{Y}}$ and more text to follow.

\bigskip

This is not:

\[ \argmax_{y \in \mathcal{Y}} \]

\end{document}

Answer 2

As long as you use the macro \DeclareMathOperator* (provided by the amsmath package) to declare the operator via, say,

\DeclareMathOperator*{\argmax}{argmax}

TeX will place the argument of the operator -- here: y\in\mathcal{Y} -- below the operator itself (a) if the instruction is encountered in display-style math mode (unless overridden by a \nolimits instruction) or (b) if the operator instruction is followed by \limits while in text style (or script or scriptscript style).

This is summarized in the following table. The first column shows the default behavior for the four math styles, i.e., without the use of \nolimits or \limits. The second column shows the result of overriding the default, either via \nolimits for display-style math or via \limits for the other three math styles.

\documentclass{article}
\usepackage{amsmath} % for '\DeclareMathOperator*' macro
\DeclareMathOperator*{\argmax}{argmax}

\usepackage{array} % for '\newcolumntype' macro
\newcolumntype{L}{>{$}l<{$}}

\begin{document}

\renewcommand\arraystretch{1.5} % just for this example
\begin{tabular}{ LL >{\ttfamily}l }
  \displaystyle \argmax_{y\in\mathcal{Y}} 
& \displaystyle \argmax\nolimits_{y\in\mathcal{Y}} 
& \string\displaystyle \\

  \argmax_{y\in\mathcal{Y}} % '\textstyle' is the default
& \argmax\limits_{y\in\mathcal{Y}}
& \string\textstyle \\

  \scriptstyle \argmax_{y\in\mathcal{Y}} 
& \scriptstyle \argmax\limits_{y\in\mathcal{Y}} 
& \string\scriptstyle \\

  \scriptscriptstyle \argmax_{y\in\mathcal{Y}}
& \scriptscriptstyle \argmax\limits_{y\in\mathcal{Y}} 
& \string\scriptscriptstyle 
\end{tabular}
\end{document}