DCP error/ Expreesion in objective function must be real

1

Hey I am trying to solve SDP problem
max tr(AZ)
s.t diag(Z)=1
Z is semidefinite matrix

cvx_begin sdp
 variable Z(n,n); 
 maximize real(trace((phi{m-1}*Z)));
 subject to
     diag(Z)==1;
     Z==semidefinite(n); cvx_end

Without word real in objective function it was giving error -"Expressions in objective functions must be real."
So i made keyword real. But I think i might be loosing some information in complex part.
So I used keyword ‘abs’ instead of ‘real’ but now the error is "Disciplined convex programming error:
Cannot maximize a(n) convex expression"
I am trying to maximize SINR which is my real problem and not atall familiar with optimization. This code snippet is just small part and I need this Z to further formulate. Since I think rest of my MATLAB code is fine. I think I might be loosing some information in this real(trace(A*Z))
Thanks in advance

1 Like
2

You shouldn’t be getting the real warning unless phi is complex. And if that is complex, in all likelihood, your variable Z should be, too, and you should be using a complex semidefinite constraint. The easiest way to do that is simply to declare

variable Z(n,n) hermitian

and also change the semidefinite constraint to

Z >= 0

Since you are using SDP mode, CVX will automatically convert this to a hermitian_semidefinite constraint.

You are still going to need real in there even if this is the case.

3

Phi is complex. Does that mean objective function has to be real. Why cant i take absolute value to make it real? that way i can have information from imaginary part as well. By specifying Z to be hermitian final SINR further diverges from correct value.

4

Further You can see objective funtion with A complex. Is code correct for such statement. As if this part is correct then I can start looking for other parts of my code.

5

Complex objective functions make no sense. (How do you maximize or minimize a complex value?) As for why you cannot take the absolute value, read the FAQ).