I would appreciate some help with this problem:
$R$ is a positive semidefinite matrix $\in{R}^{n\times n}$, $A \in{R}^{n\times m}$.
I need to formulate this optimization problem as semidefinite programming:
maximize $tr\left(({{A}^{T}{R}^{-1}A)}^{-1}\right)$
subject to $\|{r}_i-{c}_i\| \leq{\rho}_i$,
where ${c}_i$ and ${\rho}_i$ are given vectors and scalars, respectively, and ${r}_i$ = $\begin{bmatrix} {R}_{1i}\\{R}_{2i} \\.\\.\\.\\ {R}_{ii} \end{bmatrix}$, $i = 1,...,n$.
I got a hint that it is useful to use Schur complement, but I have no idea how to solve this.