How can I transform this optimization problem into a convex optimization problem?

I’m trying to solve the following optimization problem:

I was able to write the numerator of the objective function as follows:

But, I don’t know how I can get rid of the |\alpha| in the denominator. I also thought about adding constraint in the form of an epigraph, but it didn’t help.

I really appreciate any help.

if your problem is not convex, i dont think using epigraph can make it convex. if it is not convex, then it can’t be expressed by cvx.