My optimization program is max sum(-log(1+1/x)-y), but cvx dont allow the form like this log(1+1/x). I try to replace it with log(1+inv_pos(x)), but it still doesnt work. Some one can help me? Please!
-log(1+1/x) is convex for x < -1. Even if you have a constraint disallowing x < -1, log(1+1/x) won;t be accepted by CVX.
Thank you very much for your reply 
@canhui Well, this is thread is kind of old, but now that is has been bumped, I will point out that this can be handled, assuming x > 0, per the last line of the table in section 5.2.10 of https://docs.mosek.com/modeling-cookbook/expo.html (you need to adjust for the different convention (factor of sqrt(2)) used for rotated quadratic cone in the Mosek Cookbook vs. that used in CVX’s rotated_lorentz).