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We present an efficient approach for cross-layer optimization of a class of wireless networks equipped with multi-user detectors. For a given network, the method provides the optimal operation of transport, routing and radio link layers as well as the optimal coordination across the layers. The algorithm combines a column generation procedure with an optimal greedy resource allocation scheme into a powerful numerical method for computing the performance limits for networks of significant sizes. The method is applied to a simple network scenario and performance benefits of multi-user detectors and cross-layer coordination over alternative schemes are investigated.