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Traffic Engineering application to the cross-layer design of Multiple Access Interference (MAI)-affected powerlimited wireless networks, when Quality of Service constraints are also present, leads to deal with nonconvex resource allocation problems. Although several manageable-complexity solutions have been proposed, they are based on specific capacity functions and, generally, fail to provide reliable results in low-SINR (Signal to Interference plus Noise Ratio) scenarios. We develop a two-level decomposition that is able to find the optimal solution of a wide nonconvex cross-layer problem, which combines user utility, flow control, QoS multipath routing,Medium Access Control (MAC) design and power control, by means of a suitable relaxed convex version of its comprising flow control and power-allocation sub-problems. Sufficient conditions for the equivalence of the primary (nonconvex) problem and its related (convex) version are provided. Moreover, we develop a distributed, iterative, asynchronous algorithm for computing the solution of the overall nonconvex resource allocation problem, that is able to (quickly) self-adapt to possible network time evolutions (as, for example, node failure events) and, most importantly, that may be implemented on top of connectionless networking platforms. Actual performance of the overall proposed solution and its robustness against node-failure events are numerically tested and compared with the corresponding ones of Destination Sequenced Distance Vector-based single-path routing algorithms.