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Efficiently transmitting data in wireless networks requires an integrated routing and radio resource allocation strategy. An initial observation that suggest dual decomposition to be a worthwhile approach is that the network flow variables for routing and the communication variables for resource allocation are only coupled through link capacities. With dual decomposition we split routing and resource allocation up in two separate subproblems and coordinate the solutions by solving a master dual problem. In this paper, we suggest to solve the master dual problem iteratively by using Aitken's method for an update of the dual variables. In contrast to former proposed subgradient methods, we accelerate the iteration process for achieving an optimum solution. This results in significant less complexity, but still facilitating distributed implementation. Beside describing the application of Aitken's method to simultaneous routing and resource allocation we also give necessary conditions for optimality, and show results for data transmission in a wireless mesh network being optimized in a proportional fair manner.