Max sum(-log(1+1/x)-y)

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 :grinning:

@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 (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).