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We consider the problem of finding the jointly optimal end-to-end communication rates, routing, power allocation and transmission scheduling for wireless networks. We focus on throughput and fairness between end-to-end rates and formulate the associated cross-layer design problem as a nonlinear mathematical program. We develop a specialized solution method, based on a nonlinear column generation technique, that applies to a wide range of media access schemes and converges to the optimal solution in a finite number of steps. The approach is applied to a large set of sample networks and the influence of power control, spatial reuse, routing strategies and variable transmission rates on network performance is discussed.