  We address the problem of interference management and power control in terms
of maximization of a general utility function. For the utility functions under
consideration, we propose a power control algorithm based on a fixed-point
iteration; further, we prove local convergence of the algorithm in the
neighborhood of the optimal power vector. Our algorithm has several benefits
over the previously studied works in the literature: first, the algorithm can
be applied to problems other than network utility maximization (NUM), e.g.,
power control in a relay network; second, for a network with $N$ wireless
transmitters, the computational complexity of the proposed algorithm is
$\mathcal{O}(N^2)$ calculations per iteration (significantly smaller than the
$\mathcal{O}(N^3) $ calculations for Newton's iterations or gradient descent
approaches). Furthermore, the algorithm converges very fast (usually in less
than 15 iterations), and in particular, if initialized close to the optimal
solution, the convergence speed is much faster. This suggests the potential of
tracking variations in slowly fading channels. Finally, when implemented in a
distributed fashion, the algorithm attains the optimal power vector with a
signaling/computational complexity of only $\mathcal{O}(N)$ at each node.
