Nonlinear model predictive control is a popular control methodology which can seamlessly handle nonlinear dynamic, multiple inputs and constraints. It is advantageous whenever references are available ahead of time as it works by predicting state trajectories. This is a strong advantage when tracking trajectory as the vehicle can often anticipates on the incoming path profile. Despite those benefits, it is still not widely deployed. One of the main reason is that off-the-shelf available solvers are not specialized for embedded constraints. This paper is interested in presenting an efficient solver which combines a damped Newton solver with adjoint methods. This leads to a solution with moderate computational and memory requirements. The solver is used to design a lateral predictive controller running at 100 Hz with a 1 s prediction horizon, which has been validated on a real prototype vehicle.