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.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 1 Dec 2011|
- Characterization of d.c. functions
- Generalized convexity
- d.c. functions
Ginchev, I., & Martínez-Legaz, J. E. (2011). Characterization of d.c. functions in terms of quasidifferentials. Nonlinear Analysis, Theory, Methods and Applications, 74, 6781-6787. https://doi.org/10.1016/j.na.2011.07.003