The goal of the paper is to present a decomposed approach to optimization of inter-domain routing in IP networks. A problem of maximizing the total amount of traffic carried in an inter-domain network is formulated as a linear programme. Using Lagrangean relaxation the problem is decomposed with respect to individual domains. A resolution method based on subgradient optimization combined with recovering of a near optimal primal solution is discussed. Effectiveness of the method for the case of synchronized local intra-domain computations is tested using two different subgradient optimization algorithms: a divergent series algorithm and a proximal bundle algorithm. The issue of implementing such a method in a distributed networkwide process of routing optimization which could be run in the control plane of the network using the existing EGP protocols is considered. Two schemes for such decomposed optimization involving only partial synchronization of local intra-domain computations are discussed.