测试latex

\[
{\left\{ \begin{array}{l}\min \left( \frac{1 }{2 }\sum _{i =1 }^{n }\sum _{j =1 }^{n }\alpha _{i }\alpha _{j }y _{i }y _{j }{x _{i }}^{T }x _{j }\; \; -\sum _{i =1 }^{n }\alpha _{i }\; \right) \, \\
\\
\qquad \sum _{i =1 }^{n }y _{i }\alpha _{i }\ =0 \\
\\
\qquad \alpha _{i }\geq 0 ,1 \leq i \leq n \end{array} \right. }
\]