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
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