We present the analysis of the steady state backoff problem with state and dynamic constraints of a non-linear chemical process described by almost 3000 differential algebraic equations. The dynamic optimization is carried out using a new approach based on an SQP algorithm for semi-infinite non-linear programming problems. The system equations are integrated with an implicit Runge-Kutta method and 'reduced' gradients are evaluated by adjoint equations. The high performance of the algorithm is analysed and compared to fully non-linear programming proposals in which discretized system equations are treated as general non-linear equality constraints.