Given a directed graph with capacities on each arc and given a set of commodities, the QoS constrained Routing Problem (QCRP) consists in routing each commodity while respecting a endtoend upper bound on the delay for each packet. This problem is NP-hard and we propose an augmented Lagrangean approach to solve it. A flow deviation algorithm as well as a projected gradient method are proposed to solve the inner problem in the augmented Lagrangean approach. The delay and the load functions are approximated either by an analytical function or by a neural network. Computational results are reported to show the effectiveness of the projected gradient method and the neural network approximation.