  Utility-based power allocation in wireless ad-hoc networks is inherently
nonconvex because of the global coupling induced by the co-channel
interference. To tackle this challenge, we first show that the globally optimal
point lies on the boundary of the feasible region, which is utilized as a basis
to transform the utility maximization problem into an equivalent max-min
problem with more structure. By using extended duality theory, penalty
multipliers are introduced for penalizing the constraint violations, and the
minimum weighted utility maximization problem is then decomposed into
subproblems for individual users to devise a distributed stochastic power
control algorithm, where each user stochastically adjusts its target utility to
improve the total utility by simulated annealing. The proposed distributed
power control algorithm can guarantee global optimality at the cost of slow
convergence due to simulated annealing involved in the global optimization. The
geometric cooling scheme and suitable penalty parameters are used to improve
the convergence rate. Next, by integrating the stochastic power control
approach with the back-pressure algorithm, we develop a joint scheduling and
power allocation policy to stabilize the queueing systems. Finally, we
generalize the above distributed power control algorithms to multicast
communications, and show their global optimality for multicast traffic.
