How to express log(1+a/(xy)) in cvx?

1

i can prove that log(1+a/(xy)) is convex w,r.t. x and y when a>0,x>0,y>0

2

The methods from https://docs.mosek.com/modeling-cookbook/expo.html#log-sum-inv can be extended to this case.

Or in short

log_sum_exp([0, log(a)-log(x)-log(y)])
3

thank you very much, i will read the references carefully.