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

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)])
```

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