Abstract-In this work, we study the inter-domain traffic engineering problem with the perspective of attaining socially optimal flows across the Internet. In accordance with the twolevel (intra-and inter-AS) hierarchy that naturally exists in the Internet architecture, we use bi-level network flow decomposition to derive inter-domain traffic engineering solutions that do not require ISPs to reveal their intra-domain topologies in their information exchange with each other. The distributed solutions that we obtain through convex optimization techniques require ASes to exchange destination-specific rate information across the inter-domain links (i.e., between adjacent gateway routers belonging to different ASes), and determining the intra-domain traffic rates between the edge-routers based on the state of congestion of the edge-nodes in the AS, and the cost of traffic routing through the AS which in turn depends on the AS's intradomain routing/traffic engineering conditions. We investigate the optimality and convergence properties of these solutions through simulations on networks generated using realistic inter-and intradomain topology models.