The main purpose of the work was examining various methods of decomposition of a network optimization problem of simultaneous routing and bandwidth allocation based on Lagrangian relaxation. The problem studied is an NP-hard mixed-integer nonlinear optimization problem. Multiple formulations of the optimization problem are proposed for the problem decomposition. The decomposition methods used several problem formulations and different choices of the dualized constraints. A simple gradient coordination algorithm, cutting-plane coordination algorithm, and their more sophisticated variants were used to solve dual problems. The performance of the proposed decomposition methods was compared to the commercial solver CPLEX and a heuristic algorithm.