Solving a convex optimization problem is a big task. Yes, it can take a long time to converge. You can not minimize the time of the algorithm but what you can do is, you can change your converging threshold.
As you know, the convergence plot of convex optimization problem decrease exponentially and hence the major components are already gets covered in the starting. So, you can give a threshold (try to keep the threshold at or below 0.1) such that whenever your error value gets below the threshold then stop the algorithm.