I believe this is a convex optimization problem provided an and bn are both >= 0… I think a similar reformulation to that used by @Michal_Adamaszek at Can CVX solve this kind of function {x-log(1+0.01*x/(x+1))} should be possible. In particular, see my post Can CVX solve this kind of function {x-log(1+0.01*x/(x+1))} .