A New Distributed DC-Programming Method and its Applications

TL;DR

This paper introduces a new distributed optimization framework for Difference Convex (DC) functions, enabling scalable algorithms with convergence guarantees applicable to various multiuser problems in signal processing, communications, and networking.

Contribution

It develops a novel inexact best-response-like algorithm for DC programming with provable convergence, and demonstrates its effectiveness in resource allocation and sum-rate maximization tasks.

Findings

Algorithms achieve performance close to centralized methods.

Framework is applicable to multiuser DC problems in multiple domains.

Distributed schemes converge to stationary solutions.

Abstract

We propose a novel decomposition framework for the distributed optimization of Difference Convex (DC)-type nonseparable sum-utility functions subject to coupling convex constraints. A major contribution of the paper is to develop for the first time a class of (inexact) best-response-like algorithms with provable convergence, where a suitably convexified version of the original DC program is iteratively solved. The main feature of the proposed successive convex approximation method is its decomposability structure across the users, which leads naturally to distributed algorithms in the primal and/or dual domain. The proposed framework is applicable to a variety of multiuser DC problems in different areas, ranging from signal processing, to communications and networking. As a case study, in the second part of the paper we focus on two examples, namely: i) a novel resource allocation problem in the emerging area of cooperative physical layer security; ii) and the renowned sum-rate maximization of MIMO Cognitive Radio networks. Our contribution in this context is to devise a class of easy-to-implement distributed algorithms with provable convergence to stationary solution of such problems. Numerical results show that the proposed distributed schemes reach performance close to (and sometimes better than) that of centralized methods.