A dynamic optimization strategy is developed that makes use of existing differential-algebraic equation solvers and nonlinear programming strategies. In contrast to current dynamic optimization approaches, this approach applies an adjoint strategy for the calculation of objective function and constraint gradients. Furthermore, we consider two aggregation approaches, the Kreisselmeier-Steinhauser function and the smoothed penalty function, for state variable constraints. The advantage of this aggregation is to reduce the burden in the calculation of the adjoint system. The resulting implementation has a significant advantage over current strategies that rely on the solution of sensitivity equations, especially for large dynamic optimization problems. Performance of this approach is demonstrated on several dynamic optimization problems in process engineering.