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Advanced Computational Methods for Knowledge Engineering pp 15–35Cite as

DC Programming and DCA for General DC Programs

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Part of the book series: Advances in Intelligent Systems and Computing ((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.

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Authors and Affiliations

  1. Laboratory of Theorical and Applied computer Science LITA EA 3097, University of Lorraine, Ile du Saulcy, Metz, 57045, France

    Hoai An Le Thi

  2. Department of Mathematics, University of Quynhon, 170 An Duong Vuong, Quy Nhon, Vietnam

    Van Ngai Huynh

  3. Laboratory of Mathematics, INSA - Rouen, University of Normandie, 76801, Saint Etienne du Rouvray, France

    Tao Pham Dinh

Authors
  1. Hoai An Le Thi
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  2. Van Ngai Huynh
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  3. Tao Pham Dinh
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Correspondence to Hoai An Le Thi .

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Editors and Affiliations

  1. Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, Hungary

    Tien van Do

  2. Ile du Saulcy, LITA, UFR MIM, Metz, France

    Hoai An Le Thi

  3. Institute of Informatics, Wrocław University of Technology, Wrocław, Poland

    Ngoc Thanh Nguyen

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Le Thi, H.A., Huynh, V.N., Dinh, T.P. (2014). DC Programming and DCA for General DC Programs. In: van Do, T., Thi, H., Nguyen, N. (eds) Advanced Computational Methods for Knowledge Engineering. Advances in Intelligent Systems and Computing, vol 282. Springer, Cham. https://doi.org/10.1007/978-3-319-06569-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-06569-4_2

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