Dear All, I have the following matrix structure for my problem:

```
variable W1(6,6) hermitian semidefinite
variable W2(6,6) hermitian semidefinite
variable W3(6,6) hermitian semidefinite
W = [ W1(1:3,1:3) W1(1:3,4:6) oo oo
W1(4:6,1:3) W1(4:6,4:6) W2(1:3,4:6) oo
oo W2(4:6,1:3) W2(4:6,4:6) W3(1:3,4:6)
oo oo W3(4:6,1:3) W3(4:6,4:6) ];
minimize (real(trace(A*W)) + real(trace(B*W)) + real(trace(C*W)) )
subject to
W1(4:6,4:6) == W2(1:3,1:3);
W2(4:6,4:6) == W3(1:3,1:3);
W1 >= 0; W2 >= 0; W3 >= 0;
```

My question is if I want to construct the W1, W2 and W3 matrixes by using smaller Wij matrixes and each Wij is 3 by 3 matrix and rank-1 matrix.

How can I do that and what constraints should I put on my new Wij matrixes?

Thanks in advance for any help.