How to express this formula in CVX？

1

The specific formula is as follows:
formula
Where T is optimize variable, and T is an M*N matrix, U is a given matrix, alpha_0 is a complex number. Re is the operation which takes the real part of the complex number.

My MATLAB code is as follows:

image
image710×40 3.8 KB

The error reason is
image

It looks like a common mistake. So, how to solve this problem in CVX? I hope someone can provide an answer, I would greatly appreciate it！

2

I think
real(alpha0'*[1,1i])*square_pos(norm(U'*T,'fro'))
should work.

CVX doesn’t know how to deal with complex times convex (or concave), because that is neither convex nor concave. My rearrangement avoids that.

3

It really works. Thank you very much.