What I want to do is to include two lines at the begging in an one-line equation, just like in the following picture.

Does anyone have any idea in order to achieve it? Thanks a lot.
What I want to do is to include two lines at the begging in an one-line equation, just like in the following picture.

Does anyone have any idea in order to achieve it? Thanks a lot.

Please always post a complete document not just a fragment:
\documentclass[12pt]{article}
\begin{document}
\[
\max_{x\in\mathcal{J}(k)}\left\{ \sum_a^b something \middle| something\right\}
\]
\end{document}
\middle| needs spacing around it. My solution to a similar problem http://tex.stackexchange.com/a/167749/3929
– daleif
Apr 02 '14 at 14:04
something shouldn't be set in math italic, but I decided not to address those here and concentrate on the question about the subscript to max.
– David Carlisle
Apr 02 '14 at 14:09
Using mathtools (that loads amsmathanyway) and its DeclarePairedDelimiterX command, you can have a better spacing for |, and a better control on the size of the braces:
\documentclass[12pt,a4paper,leqno]{article}
\usepackage[utf8]{inputenc}
\usepackage{amssymb, mathtools}
\usepackage{textcomp}
\DeclarePairedDelimiterX{\set}[2]{\{}{\}}{#1 \delimsize\vert #2}
\newcommand*\Set[1]{\set*{#1}}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\let\emptyset\varnothing
\begin{document}
\begin{align}
\tag*{With \texttt{\textbackslash Big}:} & \max_{\mathbf x \in \mathcal J(\mathbf K)}\!{\set[\Big]{\sum_{i\in I}\mathcal G_{i \abs{C_i}}(\mathbf{\Pi}_i, y_i, \emptyset)}{(\mathbf\Pi, y_i)\in \mathcal N(\mathbf x_i)}} \\
\tag*{With \texttt{\textbackslash bigg}:} & \max_{\mathbf x \in \mathcal J(\mathbf K)}\!{\set[\bigg]{\sum_{i\in I}\mathcal G_{i \abs{C_i}}(\mathbf{\Pi}_i, y_i, \emptyset)}{(\mathbf\Pi, y_i)\in \mathcal N(\mathbf x_i)}}\\
\tag*{With an implicit \texttt{\textbackslash left}:} & \max_{\mathbf x \in \mathcal J(\mathbf K)}\!{\Set{\sum_{i\in I}\mathcal G_{i \abs{C_i}}(\mathbf{\Pi}_i, y_i, \emptyset)}{(\mathbf\Pi, y_i)\in \mathcal N(\mathbf x_i)}}
\end{align}
\end{document}

\max_{x\in\mathcal{J}(k)}\left\{...– David Carlisle Apr 02 '14 at 13:27\maxrequiresamsmath. for a more general discussion of math operators, see newcommand vs. DeclareMathOperator. for a list of operators defined in this way, see theamsmathdocumentation --texdoc amsmathon a tex live system. – barbara beeton Apr 02 '14 at 13:32amsmathmeans that you need\usepackage{amsmath}in the preamble of your document. – Steven B. Segletes Apr 02 '14 at 13:34latex \\show\\max:-) – David Carlisle Apr 02 '14 at 13:46grepbut didn't search for the "correct" string.) even so, usingamsmathif one has much math in a document isn't a bad idea. – barbara beeton Apr 02 '14 at 13:57braketpackage; How to automatically resize the vertical bar in a set comprehension? – Werner Apr 02 '14 at 15:51