  Utility (e.g., sum-rate) maximization for multiantenna broadcast and
interference channels (with one antenna at the receivers) is known to be in
general a non-convex problem, if one limits the scope to linear (beamforming)
strategies at transmitter and receivers. In this paper, it is shown that, under
some standard assumptions, most notably that the utility function is decreasing
with the interference levels at the receivers, a global optimal solution can be
found with reduced complexity via a suitably designed Branch-and-Bound method.
Although infeasible for real-time implementation, this procedure enables a
non-heuristic and systematic assessment of suboptimal techniques. A suboptimal
strategy is then proposed that, when applied to sum-rate maximization, reduces
to the well-known distributed pricing techniques. Finally, numerical results
are provided that compare global optimal solutions with suboptimal (pricing)
techniques for sum-rate maximization problems, leading to insight into issues
such as the robustness against bad initializations.
