Computing B-Stationary Points of Nonsmooth DC Programs

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) cl...

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Bibliographic Details
Published in:Mathematics of operations research 2017-02, Vol.42 (1), p.95-118
Main Authors: Pang, Jong-Shi, Razaviyayn, Meisam, Alvarado, Alberth
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Bouligand derivatives
Communications systems
Computation
Convergence
Convex programming
Cybersecurity
Data security
DC algorithm
DC constraints
Digital communications
nonsmooth DC programming
Operations research
Optimization
Program verification (computers)
randomization
Secrecy aspects
stationary solutions
Studies
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Summary: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.
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.2016.0795