A. I just wonder why we cannot do that. First of all the q-function can be expressed through the exponential functions as in the Craig expression
Thus since CVX can handle the exponential function, we can do the same for q-function as well.
I think that a few code lines defining the q-function based on the exponential functions can do the trick. Is it true?
B. I mean we can do it like that (my MatLab code)
stepsize = 0.001;
ang = 0:stepsize:(pi/2);
[~,sizea] = size(ang);
Now to compute q function at a value x, we can just do
q_approx = stepsize * 1/pi * sum(exp(-x^2./(2*sin(ang).^2)));
We know that exp(-y) is concave, and the sum of concave functions are concave. So q_approx is concave. Note that exp can be expressed in CVX. Thus we can certain add q_approx to the core of CVX as well. Just need to define a precision parameter to specify stepsize.