Characterization of d.c. functions in terms of quasidifferentials

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A characterization of d.c. functions f:Ω→R in terms of the quasidifferentials of f is obtained, where Ω is an open convex set in a real Banach space. Recall that f is called d.c. (difference of convex) if it can be represented as a difference of two finite convex functions. The relation of the obtained results with known characterizations is discussed, specifically the ones from [R. Ellaia, A. Hassouni, Characterization of nonsmooth functions through their generalized gradients, Optimization 22 (1991), 401416] in the finite-dimensional case and [A. Elhilali Alaoui, Caractérisation des fonctions DC, Ann. Sci. Math. Québec 20 (1996), 113] in the case of a Banach space. © 2011 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)6781-6787
JournalNonlinear Analysis, Theory, Methods and Applications
Publication statusPublished - 1 Dec 2011


  • Characterization of d.c. functions
  • Generalized convexity
  • Quasidifferentials
  • d.c. functions


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