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Characterization of D. C. functions. (Caractérisation des fonctions D. C.) (French. Extended English abstract) Zbl 0915.49014
Consider a real-valued locally Lipschitz function \(f\) defined over a Banach space. This paper discusses the possibility of writing \(f\) as the difference of two convex functions. It is shown that \(f\) admits such a representation if and only if its Clarke subdifferential satisfies a suitable generalized monotonicity assumption. The author extends a result by R. Ellaia and A. Hassouni [Optimization 22, No. 3, 401-416 (1991; Zbl 0734.49005)].
Reviewer: A.Seeger (Avignon)

49J52 Nonsmooth analysis
90C26 Nonconvex programming, global optimization
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
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