  Motivated by a class of applied problems arising from physical layer based
security in a digital communication system, in particular, by a secrecy
sum-rate maximization problem, this paper studies a nonsmooth,
difference-of-convex (dc) minimization problem. The contributions of this paper
are: (i) clarify several kinds of stationary solutions and their relations;
(ii) develop and establish the convergence of a novel algorithm for computing a
d-stationary solution of a problem with a convex feasible set that is arguably
the sharpest kind among the various stationary solutions; (iii) extend the
algorithm in several directions including: a randomized choice of the
subproblems that could help the practical convergence of the algorithm, a
distributed penalty approach for problems whose objective functions are sums of
dc functions, and problems with a specially structured (nonconvex) dc
constraint. For the latter class of problems, a pointwise Slater constraint
qualification is introduced that facilitates the verification and computation
of a B(ouligand)-stationary point.
