How to write d-log(1+k/x)>=-δ in CVX

1

How to write:d-log(1+k/x)>=-δ,where k>0,δ>0 and k and δ are constants .And in this constraint,x and d are all variables >= 0 .thanks.

2

You should be able to adapt the last line of the table in section 5.2.10 of https://docs.mosek.com/modeling-cookbook/expo.html#modeling-with-the-exponential-cone . You will need to take account for the sqrt(2) factor difference between how that link defines rotated quadratic cone and how CVX’s rotated_lorentz does.

3

Thank you very much for your answer. However I’m not very familiar with Sets of CVX,I don’t know how to write it in matlab, would you please show me the CVX code?

4

exp_cone constraint needs to be written:
{x,y,z} == exponential(1)

rotated_lorentz constraint needs to be written:
{x,y,z} == rotated_lorentz(1)

I will leave it to you as an exercise to figure out the correct arguments to use.