# Function Composition

I have a function f(x,y) for x \in R^{2} and y > 0. It is the following: f(x,y) = (\norm(x)^{3})/(y^2), where \norm is l-2. I’m looking at a research paper that utilized CVX and had this as a cost function term. Is there any way I can use compositions of built-in functions to represent this?

I think you can introduce a new variable z and add the constraint norm(x) <= z, then use @Michal_Adamaszek 's solution from How can I write this kind of constraint in cvx .

Putting it altogether, and in order to deconflict variable name, substituting t for x in my code for that solution in the last post of that thread, we get, if I haven’t made a mistake,

variables x(2) y z s t
norm(x) <= z
{z,s,y} == rotated_lorentz(1)
{s,t,z} == rotated_lorentz(1)


Then use t in place of norm(x)^3/y^2

Yes, I think this should work. Much thanks!