  Achieving weighted throughput maximization (WTM) through power control has
been a long standing open problem in interference-limited wireless networks.
The complicated coupling between the mutual interferences of links gives rise
to a non-convex optimization problem. Previous work has considered the WTM
problem in the high signal to interference-and-noise ratio (SINR) regime, where
the problem can be approximated and transformed into a convex optimization
problem through proper change of variables. In the general SINR regime,
however, the approximation and transformation approach does not work. This
paper proposes an algorithm, MAPEL, which globally converges to a global
optimal solution of the WTM problem in the general SINR regime. The MAPEL
algorithm is designed based on three key observations of the WTM problem: (1)
the objective function is monotonically increasing in SINR, (2) the objective
function can be transformed into a product of exponentiated linear fraction
functions, and (3) the feasible set of the equivalent transformed problem is
always normal although not necessarily convex. The MAPLE algorithm finds the
desired optimal power control solution by constructing a series of polyblocks
that approximate the feasible SINR region in increasing precision. Furthermore,
by tuning the approximation factor in MAPEL, we could engineer a desirable
tradeoff between optimality and convergence time. MAPEL provides an important
benchmark for performance evaluation of other heuristic algorithms targeting
the same problem. With the help of MAPEL, we evaluate the performance of
several respective algorithms through extensive simulations.
