Optimization Problems (\minimize, \maximize, \subjectto)
Macro Code
% ╭──────────────────────────────────────────────╮
% │ Optimization Problems │
% ╰──────────────────────────────────────────────╯
% Requires the amsmath package, which provides
% "\DeclareMathOperator" and "\DeclareMathOperator*".
% Example usage:
% \begin{align*}
% \minimize_{x \in \reals^n} \quad & f(x) \\
% \subjectto \quad & Ax \leq 0 \\
% & Bx = 0.
% \end{align*}
\DeclareMathOperator*{\minimize}{minimize}
\DeclareMathOperator*{\maximize}{maximize}
\DeclareMathOperator {\subjectto}{subject~to}
% Aliases for \maximize and \minimize with British spelling.
\let\minimise=\minimize
\let\maximise=\maximize
I define \minimize, \maximize, and \subjectto as math operators using the amsmath package's macros \DeclareMathOperator and \DeclareMathOperator* (the resulting macros are equivalent to placing \operatorname*{minimize} in the body of your document). Defining the macros as math operators ensures that the font matches the roman math font (cf. using \text{minimize} which will become italicized when used in the body of a theorem), and gives us control over the placement of "limits" on the text, e.g., "\minimize_{x \in \reals}". In particular, using \DeclareMathOperator* instead of \DeclareMathOperator causes subscripts to be placed below the text in display equations, so \[\minimize_{x \in \reals}\] is rendered as
$$\operatorname*{minimize}_{x \in \reals}$$
instead of
$$\operatorname{minimize}_{x \in \reals}.$$
For inline equations, limits are still placed to the side, e.g., "$\operatorname*{minimize}_{x \in \reals}$".
For \subjectto, we use a fixed-width nonbreaking space "~" in \operatorname to preserve the space in the name, since \operatorname gobbles regular spaces.
See “Minimize” vs. “Min” in Optimization Problems for discussion of it is better to not use "\min" when writing optimization problems.
For the Britishly-inclined, I have included aliases \minimise and \maximise. Depending on the publication venue, you can change the spelling in the definitions of "minimize" and "maximize", but to enforce consistency, I advise against defining macros that insert different variants of the spelling.
Examples
| Code | Output |
|---|---|
\begin{align*}
\minimize_{x \in \reals^n} \quad & f(x) \\
\subjectto \quad & Ax \leq 0 \\
& Bx = 0.
\end{align*}
|
$$\begin{align*} \operatorname*{minimize}_{x \in \reals^n} \quad & f(x) \\ \operatorname{subject~to} \quad & Ax \leq 0 \\ & Bx = 0. \end{align*}$$ |