How does CVX deal with complex optimization problems?

I’m using cvx in MatLab to deal with LASSO fitting.
I want to know how does cvx deal with complex fitting.
As I know there’re many methods:

Can someone tell me what does cvx do in the background, like split the real part and imagine part and optimize the objective function, or?

Thanks a lot !

The main part of my code is below,

lambda = 2;

** variable x(121,1) complex;**
** minimize (norm(D2x-target)+lambdanorm(x,1));**

D2 is a dictionary matrix (complex value).
target is my fitting target (complex value).
And don’t care about the dimension of variables, they are okay.