  We present a unified analytical framework within which power control, rate
allocation, routing, and congestion control for wireless networks can be
optimized in a coherent and integrated manner. We consider a multi-commodity
flow model with an interference-limited physical-layer scheme in which power
control and routing variables are chosen to minimize the sum of convex link
costs reflecting, for instance, queuing delay. Distributed network algorithms
where joint power control and routing are performed on a node-by-node basis are
presented. We show that with appropriately chosen parameters, these algorithms
iteratively converge to the global optimum from any initial point with finite
cost. Next, we study refinements of the algorithms for more accurate link
capacity models, and extend the results to wireless networks where the
physical-layer achievable rate region is given by an arbitrary convex set, and
the link costs are strictly quasiconvex. Finally, we demonstrate that
congestion control can be seamlessly incorporated into our framework, so that
algorithms developed for power control and routing can naturally be extended to
optimize user input rates.
