Cross-layer design can significantly improve the performance of mobile ad-hoc networks (MANETs), as indicated by the flurry of recent results in the literature. Much of this work stems from the Kelly network utility maximization (NUM) framework, where convexity is crucial for developing algorithms that reach the global optimum. Unfortunately many problems are nonconvex in nature, so convex approximations are abundant. In this paper, we consider the joint optimization of source data-rates and link transmitter powers in a MANET, specifically dealing with the statistical variations of the wireless channel. In this paradigm we show that the commonly applied high-SIR convex approximation is unrealistic, so we seek to find solutions of the unmodified NUM problem. Our first result shows that the canonical formulation (previously thought to be nonconvex) is indeed a convex problem for logarithmic TCP-Vegas utilities; we then derive an algorithm reaching the global optimum. Our main result caters for the general case of strictly concave utilities, where we derive an algorithm that provably converges to the global solution of the underlying nonconvex NUM problem.