Parallel and Distributed Methods for Nonconvex Optimization--Part II: Applications

TL;DR

This paper applies a novel distributed nonconvex optimization framework to resource allocation in communication networks, demonstrating improved performance over existing centralized methods with convergence guarantees.

Contribution

It introduces distributed algorithms for complex nonconvex resource allocation problems with convergence to stationary solutions, outperforming relaxation-based schemes.

Findings

Distributed algorithms achieve higher worst-case rates.

Methods converge to d-stationary solutions.

Comparable computational complexity to existing schemes.

Abstract

In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted to the application of the framework to some resource allocation problems in communication networks. In particular, we consider two non-trivial case-study applications, namely: (generalizations of) i) the rate profile maximization in MIMO interference broadcast networks; and the ii) the max-min fair multicast multigroup beamforming problem in a multi-cell environment. We develop a new class of algorithms enjoying the following distinctive features: i) they are \emph{distributed} across the base stations (with limited signaling) and lead to subproblems whose solutions are computable in closed form; and ii) differently from current relaxation-based schemes (e.g., semidefinite relaxation), they are proved to always converge to d-stationary solutions of the aforementioned class of nonconvex problems. Numerical results show that the proposed (distributed) schemes achieve larger worst-case rates (resp. signal-to-noise interference ratios) than state-of-the-art centralized ones while having comparable computational complexity.