I’m afraid I do not think this is possible. CVX really doesn’t allow for expressions that are convex over intervals but not their entire domain.

Your inv_pos trick works for x/(c-x) because inv_pos is differentiable over its entire domain. With x/(c-x)^2, there might be a way to represent it for x\lt c, but for x\gt c there is an inflection point where the second derivative transitions from positive to negative, and this is a sign that CVX simply will be unable to handle it.