Is 1/(1 +exp(x)) solvable? Here x>0

It is easy to see 1/(1 +exp(x)) is convex when x > 0. However, the following code doesn’t work. Is there a better to rewrite the problem?

    variable x(n) nonnegative
    minimize( sum(inv_pos(1 + exp(x))) )
    subject to
        sum(inv_pos(2-x)) <= R
        x >= 1
        x < 2

No, there is not. This function cannot be represented using CVX’s rules and base functions.