  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.
