How can I solve the following semidefinite program in an analytic way?
$\displaystyle \min\sum_{i=1}^{d} \mathcal{e}_i$
$S.t\thinspace\thinspace\begin{bmatrix}\mathcal{e_1}&0&0\\\vdots&\ddots&\vdots\\0&\dots&\mathcal{e}_d\end{bmatrix}-A\succeq0$.
Where $A$ is the Adjacency Matrix of the graph