Cannot perform the operation: {complex affine} .* {convex}?

1

Code:

h = randn(N,1) + 1i*randn(N,1);
cvx_begin
   variable U(N,N,K)
   
   Ui = U(:,:,1);
   phi = h' * Ui * h;
   D = h * phi * h';
cvx_end

Error information:
Disciplined convex programming error:
Cannot perform the operation: {complex affine} .* {convex}

Error line：D = h * phi * h’;

2

I don’t know why you are getting that error. Here is what I get using CVX 2.2 (note I removed the semicolons so that CVX displays what each expression is).

   N = 4; K = 3;
   h = randn(N,1) + 1i*randn(N,1);
   cvx_begin
   variable U(N,N,K)
   
   Ui = U(:,:,1)
   phi = h' * Ui * h
   D = h * phi * h'

Output:

Ui =
    cvx real affine expression (4x4 matrix)
phi =
    cvx complex affine expression (scalar)
D =
    cvx complex affine expression (4x4 matrix)

Are you using CVX 3.0beta? If so, do not, because it is riddled with bugs which almost certainly will never be fixed. . Use CVX 2.2.

cvx_version shows the CVX version.

Or maybe that is not really the statement sequence you ran when you got the error message? Try a new MATLAB session and enter only those statements, and see what happens.

4

Thanks for your suggestions!
However, the condition for variable U is missing in the previous code.
The code is as follows:
h = randn(N,1) + 1i*randn(N,1);
cvx_begin
variable U(N,N,K) hermitian semidefinite

Ui = U(:,:,1);
phi = h’ * Ui * h;
D = h * phi * h’;
cvx_end

Error information:
Disciplined convex programming error:
Cannot perform the operation: {complex affine} .* {convex}

Error line：D = h * phi * h’;

5

My output from that is

Ui =
    cvx mixed real affine/complex affine expression (4x4 matrix)
phi =
    cvx real affine expression (scalar)
D =
    cvx complex affine expression (4x4 matrix)

The only difference from the previous output is for Ui.

It would seem that something is screwed up with your MATLAB installation. Please show the output from cvx_version. Perhaps you should remove all CVX directories (folders) from the MATLAB path, and then install CVX 2.2 in a new MATLAB session. Then try your program again.

6

Thank you for your suggestions. I will try to use the proposed method.

7

The code is as follows:
h = randn(N,1) + 1i*randn(N,1);
cvx_begin
variable U(N,N,K) hermitian semidefinite

Ui = U(:,:,1);
phi1 = h’ * Ui * h;
phi2 = pow_p(phi1,-1);
D = h * phi2 * h’;
cvx_end

Error information:
Disciplined convex programming error:
Cannot perform the operation: {complex affine} .* {convex}

Error line：D = h * phi2 * h’;

Moderator’s note: I have moved this into your existing thread on this matter

8

D violates CVX rules. CVX can’t handle {imaginary}*{convex) or {imaginary}*{concave) because those are neither concave or complex.

If h were real, CVX would accept D.

With h complex, CVX would accept real(RHS of D if it is rearranged to D = real(h * h') * phi2

I don’t know what you intend to do with D. So it is possible that the D as is in your program, but never explicitly formed, might still be compatible with a DCP-compliant convex optimization problem. But that would require not forming D, and proceeding directly to the way in which it is used, and seeing whether a DCP-compliant formulation can be created.

Your first step is to prove that your problem is a convex optimization problem. If not, CVX is not the right tool for it.

9

Thanks for your suggestions! I will check it.

10

Note that I am not suggesting you use real(h * h') * phi2. I stated that CVX would accept it. That doesn’t mean that is the correct thing to do for your intended application, which I have no idea what it is, so I can’t say whether it is a “correct” thing to do.