I am trying to solve an optimization problem with quadratic constraints of the

form

minimize\sum_{m=1}^MTr[W_m]

s.t. Tr[R_kW_k]-\gamma_k\sum_{l\neq k}^MTr(R_kW_l)>=\gamma_k\sigma^2_k

W_k>=0 , k=1,…,M

where W_i = w_iw_i^T ,w_i is (10,1) complex vectors ,R_k\in R^{10*10}, M=3

I’m trying to solve the problem in CVX!

the code is here:

```
cvx_begin quiet
variable W0(10,10) hermitian;
variable W1(10,10) hermitian;
variable W2(10,10) hermitian;
minimize (trace(W0)+trace(W1)+trace(W2)) ;
subject to
trace(R0*W0) >= gamma_1*sigma^2 + gamma_1 * (trace(R0*W1)+trace(R0*W2));
trace(R1*W1) >= gamma_2*sigma^2 + gamma_2 * (trace(R1*W0)+trace(R1*W2));
trace(R2*W2) >= gamma_3*sigma^2 + gamma_3 * (trace(R2*W1)+trace(R2*W0));
W0 == semidefinite(10);
W1 == semidefinite(10);
W2 == semidefinite(10);
cvx_end
```

W_i = w_iw_i^T ,but the answer is a real matrix,I don’t know why?

Thank you for devoting your time .