Log-sum-inv,is it right

I have a constraint which includes three variables

I had a try to rewrite the constraint in two steps.
It is my first to rewrite the constraint in equivalent form,I want to know is it right ?
Thank you !


And you need to throw a log(2) in there somewhere to account for log2 vs. log.

Thank you .Yes,I will add log(2) in somewhere.

but in your third constraint, xi and zi are all variable
how to express in cvx?

You need to declare additional CVX variables. See for instance my code snippet in Log( {convex} ) This can be extended to the case, as shown in the Mosek Modeling Cookbook, in which there are multiple inverse terms, by using vector variables.

xi is expressed in the first paper,x0, x1 ,x2,…,xu.
zi is an auxiliary variable.