  This paper studies the maximization of the weighted sum energy efficiency
(WSEE). We derive a first-order optimal algorithm applicable to a wide class of
communication scenarios exhibiting very fast convergence. We also discuss how
to leverage monotonic optimization and fractional programming to obtain a
global optimal solution at the cost of higher computational complexity. The
WSEE of interference networks is studied in detail with an application to
relay-assisted multi-cell communication. This scenario is modeled as a
non-regenerative multi-way relay channel and the achievable rate region is
derived. We apply the proposed algorithm to this scenario and compare its
performance to the global optimal algorithm. The results indicate that the
proposed algorithm often achieves the global optimal solution and is close to
it otherwise. Convergence is achieved within 10 iterations, while the global
optimal solution may require more than $10^6$ iterations.
