# How to align left bracket equation

$$\left\{ \begin{matrix} Maximiser &L(\alpha)=\sum_{i=1}^{n} \alpha_i -\sum_{i=1}^{n}\sum_{j=1}^{n}\alpha_i \alpha_j y_iy_j \textbf{x}^T\textbf{x} &\\ \text{sous contraintes} & & \\ & \sum_{i=1}^{n}\alpha_iy_i=0 \\ & \alpha_i>0& \end{matrix} \right.$$


• matrix centers each column. You might try \cases Dec 29, 2016 at 2:38

I would like to suggest that (a) the equations be typeset in display style -- done most easily by using a dcases environment -- and (b) the constraint statements be aligned on their respective inequality/equality particles -- using, say, an aligned environment. Oh, and do use \mathbf instead of \textbf while in math mode.

\documentclass{article}
\usepackage{mathtools,mathptmx}
\begin{document}
\begin{dcases} \text{Maximiser} & L(\alpha)=\sum_{i=1}^{n} \alpha_i -\sum_{i=1}^{n}\sum_{j=1}^{n}\alpha_i \alpha_j y_iy_j \mathbf{x}^T\!\mathbf{x} \\ \text{sous contraintes} & \!\begin{aligned}[t] \sum_{i=1}^{n}\alpha_iy_i&=0 \\ \forall\ i\colon\alpha_i&>0 \end{aligned} \end{dcases}
\end{document}


I wouldn't go to a new line after “sous contraintes”, but I propose both solutions.

\documentclass{article}
\usepackage{amsmath}
\usepackage{newtxtext,newtxmath}

\DeclareMathOperator{\Maximize}{\mathit{Maximiser}}
\newcommand{\subjto}{\textnormal{sous contraintes}}

\begin{document}

\left\{\begin{aligned} & \Maximize\quad L(\alpha)= \sum_{i=1}^{n} \alpha_i -\sum_{i=1}^{n}\sum_{j=1}^{n}\alpha_i \alpha_j y_iy_j \mathbf{x}^T\mathbf{x} \\ & \begin{aligned} \subjto\quad & \sum_{i=1}^{n}\alpha_iy_i=0 \\ & \forall i\colon\alpha_i>0 \end{aligned} \end{aligned}\right.

\left\{\begin{aligned} & \Maximize\quad L(\alpha)= \sum_{i=1}^{n} \alpha_i -\sum_{i=1}^{n}\sum_{j=1}^{n}\alpha_i \alpha_j y_iy_j \mathbf{x}^T\mathbf{x} \\ & \begin{aligned} \subjto\quad\\ & \sum_{i=1}^{n}\alpha_iy_i=0 \\ & \forall i\colon\alpha_i>0 \end{aligned} \end{aligned}\right.

\end{document}


Better define abstract versions of the operators, so you can easily port documents from one language to the other.

$$\label{hypersep} \begin{cases} Maximiser &L(\alpha)=\sum_{i=1}^{n} \alpha_i -\sum_{i=1}^{n}\sum_{j=1}^{n}\alpha_i \alpha_j y_iy_j \textbf{x}^T\textbf{x}\\ \text{sous contraintes} &\\ & \sum_{i=1}^{n}\alpha_iy_i=0 \\ & \alpha_i>0 \end{cases}$$


\left\{
\begin{array}{ll}
\textrm{Maximiser}
&
L(\alpha)=\sum_{i=1}^{n}\alpha_{i}-\sum_{i=1}^{n}\sum_{j=1}^{n}\alpha_{i}\alpha_{j}y_{i}y_{j}\textbf{x}^{T}\textbf{x}
\\
\textrm{sous contraintes}
&
\begin{aligned}[t]
\sum\nolimits _{i=1}^{n}\alpha_{i}y_{i}
&
=0
\\
\alpha_{i}
&
>0
\end{aligned}
\end{array}
\right.


I would add a bit of vertical space between array rows using \\[15pt] instead of simple \\: