This paper demonstrates the effectiveness of applying optimization techniques to solve traffic engineering (TE) problems in IP networks over Multiprotocol Label Switching (MPLS). Our approach models TE tasks as mathematical programming problems and proposes heuristic algorithms. Another contribution of this work is the combination of Lagrangean relaxation with heuristics to compute near-optimal solutions quickly. Numerical experiments contrast the solutions produced by our algorithm with optimal ones, which were obtained with a top-notch optimization software package. All in all, the results indicate that the Lagrangean-based routing method outperforms standard algorithms with respect to a number of performance criteria, including throughput and packet-loss rate.