How to model this in objective function

Hi there,

I get a problem with the CVX when I try to add the obj function below:

A* x* ctranspose(A)/B* x* ctranspose(B)

where x is a 3 by 3 hermitian matrix and A = [1 a^2 a], B=[1 a a^2], a= -0.5 + 0.5 * 1i * sqrt(3).

How should I model this and meet the DCP rules?

Because x is a hermitian matrix and I do a ctranspose of A therefore the product of Ax ctranspose(A) should be a scalar variable?

Many thanks for that.

That produces {real affine}/{real affine}, which is not allowed in CVX, and is non-convex.

It is a linear fractional form which potentially, depending on the rest of the program, could be reformulated as a convex problem for CVX. But that would require that the denominator always be positive, or alternatively, always be negative.

Yeah, you are right, the formulation seems like a linear fractional form and the denominator always be positive, but I have no idea about how to convert it into a convex function which CVX could accept it, by the way, the rest of my problem are all convex formulation, practically, belongs to SDP problem.

Could you give me some indication for my problem?

Many thanks,

You can read the material on linear fractional forms in . As for whether that will work with the rest of your problem, including SDP constraints, I don’t know.