Title: Resource Allocation for Wireless Networks: A Distributed Optimization Approach,
Abstract: We consider the multi-cell joint power control and scheduling problem in
cellular wireless networks as a weighted sum-rate maximization problem. This
formulation is very general and applies to a wide range of applications and QoS
requirements. The problem is inherently hard due to objective's non-convexity
and the knapsack-like constraints. Moreover, practical system requires a
distributed operation. We applied an existing algorithm proposed by Scutari et
al. in distributed optimization literature to our problem. The algorithm
performs local optimization followed by consensus update repeatedly. However,
it is not fully applicable to our problem, as it requires all decision
variables to be maintained at every base station (BS), which is impractical for
large-scale networks; also, it relies on the Lipschitz continuity of the
objective function's gradient, which does not hold here. We exploited the
nature of our objective function, and proposed a localized version of the
algorithm. Furthermore, we relaxed the requirements of Lipschitz continuity
with the proximal approximation. Convergence to local optimal solutions was
proved under some conditions. Future work includes proving the above results
from a stochastic approximation perspective, and investigating non-linear
consensus schemes to speed up the convergence.