Hi,
as in the figure,
I have a vector \bm{x} and \bm{y}, and a constraint in (3) as the sum of elementwise cubic over quad, the problem is that I do not know how to express this constraint in an acceptable way in CVX. As shown in (4) and (5) for the elementwise function, with x,y \ge 0, the Hessian is positive definite, so the left hand side of (3), as a sum of convex function, should be convex.
Many many thanks for the kind help.
Hi Michal,
Many thanks for your prompt reply and kind help. I have solved the problem based on your advice.
Yet I have two additional questions seeking for insights:

Actually for my problem, the variablex in the equation is expressed as a norms(w, 2, 2), my current solution is to redefine vector z = norms(w, 2, 2); and further define s = z^3/y^2. As such, I have introduced two more vectors to solve the problem, and I have used a for loop for the elementwise rotatedlorentz constraint, which apprears to be complicated. So I wonder if there is anything like quad_over_lin to express cubic_over_quad, in a more efficient and graceful manner.

You mentioned that “(n+1)powerovernpower should be representable by iterating quadoverlins”, I wonder if you refer to the inherent mechnism regarding the CVX itself that has nothing to do with users, or we can write our own code to implement the quad_over_lin iteration towards cubic_over_quad.
Thanks a lot.
 Maybe you can eliminate the loop if it can be vectorized but I don’t know that.
 I mean it can be modeled mathematically by extending the model from my answer and therefore can be implemented by a CVX user.
You will probably not avoid the intermediate cones because CVX only uses quadratic cones.
Hi Michal,
Many thanks for the further note. Has helped a lot.
Hello! I have the same problem about cubic over quad. My x is also the norm of one variable, could you please tell me how you handled this?