Dual Decomposition Methods for Nonlinear Resource Allocation Problems in Telecommunication Networks

We consider problems of optimal resource allocation in zonal telecommunication networks with many users. In the simplest formulation the network manager aims to distribute some homogeneous resource (say bandwidth) among users within one zone. We assume strictly convex charge and convex quadratic fee functions and present combined dual type solution methods. Next, we consider a more general problem for a multizonal wireless communication network with common capacity constraints. We obtain a convex optimization problem involving two kinds of constraints. By using the dual Lagrangian method with respect to the capacity constraint, we suggest to reduce the initial problem to a single-dimensional optimization problem, but calculation of the cost function value leads to independent solution of zonal problems, which coincide with the previous single region problem. Some results of computational experiments confirm the applicability of the new methods.