Multiline brackets around inner Minimization Problem for Maximin Optimization Problem

Question

I want to reproduce the following:

The inner min-Problem I make with a \begin{equation}\begin{aligned} inner min-Problem \end{aligned}\end{equation}

But I can't find a way to make brackets around it nor to write the max left to those brackets.

Answer 1

I propose to do it with a simple pmatrix* environment:

\documentclass{article}
\usepackage{mathtools}
\usepackage{booktabs} 
\DeclareMathOperator{\conv}{conv}

\begin{document}
\[
\max_{\lambda\ge0}\begin{pmatrix*}[l]\displaystyle
    \min_{c,x} \sum_t\sum_i c_{it} - \sum_t \lambda_t\Bigl(\sum_i A_{it}x_{it} - b_t\Bigr)\\\addlinespace%[2.5ex]
   \: \mathrm{s.t.}\enspace (c_i,x_i) \in \conv\bigl( V_{j\in J_i} X_i^j\bigr)
  \end{pmatrix*}
\]

\end{document} 

Answer 2

Welcome to TeX:SE!

Try the following:

\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\conv}{conv}

\begin{document}
\begin{equation}
\max_{\lambda\ge0}\left(
    \begin{aligned}
    \min_{c,x}    &\quad &&   \sum_t\sum_i c_{it} - \sum_t \lambda_t\biggl(\sum_i A_{it}x_{it} - b_t\biggr)\\[1ex]
    \mathrm{s.t.} &      &&   (c_i,x_i) \in \conv\Bigl( V_{j\in J_i} X_i^j\Bigr)
    \end{aligned}\right)
\end{equation}
\end{document}