This paper presents a novel optimization-based full-pose trajectory tracking method to control overactuated multi-rotor aerial vehicles with limited actuation abilities. The proposed method allocates feasible control inputs to track a reference trajectory, while ensuring the tracking of the reference position, and while tracking the closest feasible attitude. The optimization simultaneously searches for a feasible trajectory and corresponding feasible control inputs from the infinite possible solutions, while ensuring smooth control inputs. The proposed real-time algorithm is tested in extensive simulation on multiple platforms with fixed and actuated propellers. The simulation experiments show the ability of the proposed approach to exploit the complex set of feasible forces and moments of overactuated platforms while allocating smooth feasible control inputs.