Cvx formulation

Nonconvex
1

Hi all,

I will appreciate that if someone informs me how to handle the following expression in cvx:

( 1 - 1 / ( 1 + (a * x^2) / (b * y + c * z) )^2)^0.5

here the variables are x, y, and z; while a, b, and c are coefficients

Thanks in advance

2

According to my Hessian calculations (for a = b = c = x = y = z = 1), this is neither convex nor concave. And that would still be true even if either b = 0 or c = 0, and even if the square root were not there.

So I think you’'re out of luck using this in CVX.

3

Thanks for your answer. I really appreciate it.

How about using x instead of x^2? I know that the new expression is neither convex nor concave.

Is there a method to find a convex upper bound for the new expression which will be
( 1 - 1 / ( 1 + (a * x) / (b * y + c * z) )^2)^0.5

Thanks in advance

4

I suggest you re-read the link.

If you are looking for methods to provide convex bounds, this is not the right place.

5

Thank you very much.