Define a symmetic matrix $\Theta\_j\in \mathbb R^{n\times n}, \forall j \in \{1,2,\cdots,M\}$, symmetic matrices $A,S\in \mathbb R^{n\times n}$, scalar $\rho\in \mathbb R\_+$, and scalar $c\_{i,j} \in \mathbb R, \forall i \in \{1,2,\cdots,N\}, \forall j \in \{1,2,\cdots,M\}$. We have

$$
A + 
{\rho} \sum\limits\_{i=1}^N \sum\limits\_{j=1}^{M} \left({\Theta\_j}\left(\operatorname{Tr}\left({\Theta\_j} X \right) + {c\_{i,j}} \right) \right) 
+ 2\left(X^\top - S\right) = 0.
$$

Note that the matrices $\Theta\_j$ are not positive definite. I wonder how to calculate $X\in \mathbb R^{n\times n}$.