  Convex optimization is a powerful tool for resource allocation and signal
processing in wireless networks. As the network density is expected to
drastically increase in order to accommodate the exponentially growing mobile
data traffic, performance optimization problems are entering a new era
characterized by a high dimension and/or a large number of constraints, which
poses significant design and computational challenges. In this paper, we
present a novel two-stage approach to solve large-scale convex optimization
problems for dense wireless cooperative networks, which can effectively detect
infeasibility and enjoy modeling flexibility. In the proposed approach, the
original large-scale convex problem is transformed into a standard cone
programming form in the first stage via matrix stuffing, which only needs to
copy the problem parameters such as channel state information (CSI) and
quality-of-service (QoS) requirements to the pre-stored structure of the
standard form. The capability of yielding infeasibility certificates and
enabling parallel computing is achieved by solving the homogeneous self-dual
embedding of the primal-dual pair of the standard form. In the solving stage,
the operator splitting method, namely, the alternating direction method of
multipliers (ADMM), is adopted to solve the large-scale homogeneous self-dual
embedding. Compared with second-order methods, ADMM can solve large-scale
problems in parallel with modest accuracy within a reasonable amount of time.
Simulation results will demonstrate the speedup, scalability, and reliability
of the proposed framework compared with the state-of-the-art modeling
frameworks and solvers.
