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DC Programming and DCA for General DC Programs

  • Hoai An Le Thi
  • Van Ngai Huynh
  • Tao Pham Dinh
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 282)

Abstract

We present a natural extension of DC programming and DCA for modeling and solving general DC programs with DC constraints. Two resulting approaches consist in reformulating those programs as standard DC programs in order to use standard DCAs for their solutions. The first one is based on penalty techniques in DC programming, while the second linearizes concave functions in DC constraints to build convex inner approximations of the feasible set. They are proved to converge to KKT points of general DC programs under usual constraints qualifications. Both designed algorithms can be viewed as a sequence of standard DCAs with updated penalty (resp. relaxation) parameters.

Keywords

DC programming DCA DC constraints subdifferential nonsmooth penalty function constraint qualification 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Hoai An Le Thi
    • 1
  • Van Ngai Huynh
    • 2
  • Tao Pham Dinh
    • 3
  1. 1.Laboratory of Theorical and Applied computer Science LITA EA 3097University of LorraineMetzFrance
  2. 2.Department of MathematicsUniversity of QuynhonQuy NhonVietnam
  3. 3.Laboratory of Mathematics, INSA - RouenUniversity of NormandieSaint Etienne du RouvrayFrance

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