Modelling rational power functions as cones for conic quadratic programming

Modelling rational power functions as cones for conic quadratic programming

It's quite easy to find documentation online that shows that conic
quadratic programming can be used with functions that have ration powers,
such as x^(3/2). example
I can also find examples of these functions actually being modelled as
cones, for instance here in appendex B is x^(3/2)
However, what I cannot find is an explanation of how you come up with the
cones to model an arbitrary ration power function. Is there an algorithm?
Is it pulled from thin air?
For clarity, here is the example in appendix B above of X^(3/2).
Model |x|^3/2 ¡Ü t
as a conic quadratic constraint.
We initially represent it as
−z ¡Ü x ¡Ü z,
z^2
¡Ìz ¡Ü t, z ¡Ý 0
using an additional variable z. The only non-linear constraint is z^2/¡Ìz
¡Ü t, which can be
represented equivalently as
z^2 ¡Ü 2st
w^2 ¡Ü 2vr
z = v
s = w
r = 1
8
s, t, v, r ¡Ý 0,
But there is no discussion of how to get from point A to point B and I
haven't really found it discussed anywhere that I can understand...