# How to create a vertical brace in an aligned optimisation problem?

I am trying to create a vertical brace around particular constraints in an optimisation problem. A segment of my code is shown below

\begin{equation*}
\begin{aligned}
\underset{x_{ij}}{\text{minimise}} \quad & 5x_{11}+3x_{12}\\&+7x_{21}+11x_{22}\\&+15x_{31}+29x_{32}\\
\textrm{such that} \quad & x_{22}+x_{12}+x_{22}\leq 9,\\
&x_{21}+x_{42}+x_{23}\leq 5,\\
&x_{33}+x_{43}+x_{34}\leq 11,\\
\end{aligned}
\end{equation*}


The brace is to convey what the three constraints represent. An example of this is shown below

• I think you want the cases environment. – campa Nov 11 '20 at 8:23
• @campa Do you have any links that explain this? I'm unsure of this. – M B Nov 11 '20 at 8:24
• @campa Not exactly; I am not creating a piecewise function. Suppose that I have multiple contraints in my optimisation problem. If I wanted to specify that, for example, three of the contraints were "balance constraints", how could I code a vertical brace (formatted to the right) to include a description to explain this? – M B Nov 11 '20 at 8:29
• You might want to incluce a picture of what the output is supposed to be. At this point I can only guess what you are trying to achieve. – campa Nov 11 '20 at 8:33
• @campa Sure, I have done this. Does this help to clarify things? – M B Nov 11 '20 at 8:41

## 1 Answer

Something like this?

\documentclass{article}
\usepackage{mathtools} % for 'rcases' env.
\begin{document}

\begin{equation*}
\begin{aligned}
\smash[b]{\underset{x_{ij}}{\textnormal{minimise}}} \quad
&5x_{11}+3x_{12}   \\
&+7x_{21}+11x_{22} \\
&+15x_{31}+29x_{32}\\
\textnormal{such that}\quad
&\begin{rcases}
x_{22}+x_{12}+x_{22}\leq 9\,,\\
x_{21}+x_{42}+x_{23}\leq 5\,,\\
x_{33}+x_{43}+x_{34}\leq 11\,.
\end{rcases}
\cdots
\end{aligned}
\end{equation*}

\end{document}

• This is perfect. Thanks for teaching me something new. – M B Nov 11 '20 at 8:57