  Transmit power control in wireless networks has long been recognized as an
effective mechanism to mitigate co-channel interference. Due to the highly
non-convex nature, optimal power control is known to be difficult to achieve if
a system utility is to be maximized. To date, there does not yet exist a
distributed power control algorithm that maximizes any form of system utility,
despite the importance of distributed implementation for the wireless
infrastructureless networks such as ad hoc and sensor networks. This paper
fills this gap by developing a Gibbs Sampling based Asynchronous distributed
power control algorithm (referred to as GLAD). The proposed algorithm quickly
converges to the global optimal solution regardless of the concavity,
continuity, differentiability and monotonicity of the utility function. Same as
other existing distributed power control algorithms, GLAD requires extensive
message passing among all users in the network, which leads to high signaling
overhead and high processing complexity. To address this issue, this paper
further proposes a variant of the GLAD algorithm, referred to as I-GLAD, where
the prefix "I" stands for infrequent message passing. The convergence of I-GLAD
can be proved regardless of the reduction in the message passing rate. To
further reduce the processing complexity at each transmitter, we develop an
enhanced version of I-GLAD, referred to as NI-GLAD, where only the control
messages from the neighboring links are processed. Our simulation results show
that I-GLAD approximately converges to the global optimal solution regardless
of the type of the system utility function. Meanwhile, the optimality of the
solution obtained by NI-GLAD depends on the selection of the neighborhood size.
