Log-sum-inv，is it right

[Shuzhen (Shuzhen Liu)]

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 !

1. 

2.

[jackfsuia (Jack)]

How to express log(1+ sum ( 1./x ) ) in CVX?

Use the first approach in section 5.2.7 Log-sum-inv of https://docs.mosek.com/modeling-cookbook/expo.html#exponential-cone 4 by using CVX’s log_sum_exp for the ti >= … constraint, and also include the xi >= … constraint in that link as written. Prepend your x with a new first element of 1 to handle the `1+``

[Mark_L_Stone]

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

[Shuzhen (Shuzhen Liu)]

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

[Cici (Long Yusi)]

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

[Mark_L_Stone]

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.

[Shuzhen (Shuzhen Liu)]

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