Computing B-Stationary Points of Nonsmooth DC Programs

Computing B-Stationary Points of Nonsmooth DC Programs

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Article ID: iaor2017616
Volume: 42
Issue: 1
Start Page Number: 95
End Page Number: 118
Publication Date: Jan 2017
Journal: Mathematics of Operations Research
Authors: , ,
Keywords: security, optimization, programming: convex
Abstract:

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.

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