please help me solve this expression in cvx: log(1/(1+x^2)) . And log(1/(1+x^2)^2)?

x1>= log(1/(1+x2^2));x^3>= log(1/(1+x4^2)^2)

I believe `log(1+1/x^2)`

, which is convex, can be handled by using `y(i)/2`

in place of `y(i)`

in the last constraint of the 1st approach of section 3.2.7 Log-sum-in of Mosek Modeling Cookbook

In this specific case, that would be:

```
variables t x y
t >= log_sum_exp([0;y])
x >= exp(-y/2)
```

As for `x^3 >= log(1/(1+x^2)^2)`

, that is non-convex because `RHS - LHS`

is non-convex. Also, RHS is individually non-convex (x = 1 is the boundary between concavity and convexity), and LHS is individually non-concave. So, a “loser” all the way around.