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Characterization of d.c. Functions in terms of quasidifferentials. (English) Zbl 1229.90137
Summary: A characterization of d.c. functions \(f:\Omega \to \mathbb R\) in terms of the quasidifferentials of \(f\) is obtained, where \(\Omega \) 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 and A. Hassouni, Optimization 22, No.3, 401–416 (1991; Zbl 0734.49005)] in the finite-dimensional case and [A. Elhilali Alaoui, Ann. Sci. Math. Qué. 20, No.1, 1–13 (1996; Zbl 0915.49014)] in the case of a Banach space.

MSC:
90C26 Nonconvex programming, global optimization
26B25 Convexity of real functions of several variables, generalizations
49J52 Nonsmooth analysis
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