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!