1. A method for operating hierarchical software defined network (SDN) controllers, the method comprising: receiving, by a parent SDN controller, regional information from one or more child SDN controllers, wherein the parent SDN controller is at a higher tier in a hierarchical SDN network architecture than the one or more child SDN controllers, wherein each of the one or more child SDN controllers are assigned a different SDN region in an SDN domain assigned to the parent SDN controller, and wherein the parent SDN controller communicates with the child SDN controllers using an SDN protocol via an SDN control plane, the parent SDN controller and the one or more child SDN controllers all being part of the SDN control plane, the SDN domain including a first region assigned to a first child SDN controller and a second region assigned to a second child SDN controller; computing cost-based parameters in accordance with the regional information, the cost-based parameters being computed at least by estimating Lagrangian variables for a coupling constraint in accordance with the regional information, the coupling constraint being associated with an inter-region link extending between the first region and the second region; and sending, by the parent SDN controller, the cost-based parameters to the one or more child SDN controllers, wherein the cost-based parameters are configured to be used in performing distributed network resource allocation in each of different regions of the SDN domain.