I have the following maximum likelihood optimization problem:
$$ \hat{X}=\underset{X}{\text{argmax}} \left ( T_{1}X^{T}GX+T_{2}X^{T}Y \right ) \\ \text{s.t.} \left\{\begin{matrix} X\in \{\pm 1\}^{n}\\ X^{T} \mathbf{1}=0\\ \end{matrix}\right. $$ where $T_{1}$ and $T_{2}$ are constants, $Y \in\{\pm 1\}^{n}$ is a known $n\times 1$ vector, $G$ is a known $n\times n$ matrix and $X$ is a $n\times 1$ vector.
I am going to write this problem as a semi-definite programming problem. Do you know what should I do?