Operators you invent once

LaTeX ships with named operators like \sin, \log, and \max that print in upright type with correct spacing around them. It does not ship with \argmin or \argmax, even though optimization papers use them on nearly every page. If you type argmin as plain letters inside math mode, LaTeX treats it as the product of six variables: the letters come out italic, squeezed together, with no operator spacing. The fix is to declare the operator yourself, once, in the preamble.

Declaring the operator

\usepackage{amsmath}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\argmax}{arg\,max}

\[
\theta^\star = \argmin_\theta \mathcal{L}(\theta)
\]

Here is what each piece does. \DeclareMathOperator comes from amsmath and creates a new command whose argument is typeset as operator text: upright roman letters, with the spacing rules LaTeX already applies to \max and \lim. The first argument is the command name you will type, the second is the text that actually prints. The \, inside arg\,min inserts a thin space between the two words, which reads better than running them together.

The star after \DeclareMathOperator matters. A starred declaration makes the operator behave like \lim: in display math, anything you attach with _ sits directly underneath the operator instead of trailing to its lower right. That is exactly what you want for \argmin_\theta, where the variable being optimized over should appear below. Without the star, the subscript stays at the side, which is the convention for operators like \log_2. In inline math the subscript stays at the side either way, to avoid stretching the line height.

Reusing the pattern

The same technique covers any operator your field uses that LaTeX does not know about. A few common ones:

\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator*{\esssup}{ess\,sup}

Notice that \tr, \rank, and \diag are unstarred because their subscripts, when they have any, belong at the side. Only limit-style operators such as \esssup get the star.

Declaring operators in the preamble instead of writing \mathrm{argmin} inline pays off twice. Your notation stays consistent across the whole document, and if a journal asks for a different rendering, you change one line instead of hunting through every equation. You can try the declaration and the display line together in the live playground to see how the starred subscript placement behaves.

A common mistake: declaring an operator whose name collides with an existing command, such as \max or \deg. LaTeX will stop with an “already defined” error. Pick a fresh name, or use \renewcommand only if you genuinely intend to replace the original.