Hello,

I am trying to solve this optimization problem. And I know the mistake is because CVX treats all entries separately therefore it is not convex. But I don’t know how to change the code in order to make it work. Does anybody have a hint how to proceed?

Note: X_1T_1 is n by T, U_01T_1 is m by T

MATLAB-code:

```
Q_x=eye(T,n);
R=eye(m);
I=eye(n);
X_1T_1=P(1:n,2:T+1);
cvx_begin
variables G_k(T,n) W(n,T) X(m,m)
minimize trace(Q_x*W)+ trace(X)
subject to
X_1T_1*G_k*W*G_k'*X_1T_1'-W+I<=zeros(n);
-W<=-I;
-X+sqrt(R)*U_01T_1 *G_k *W*G_k'*U_01T_1'*sqrt(R)<= zeros(m);
X_0T_1*G_k == I
cvx_end
```