## 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)

### MSC:

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

Zbl 0734.49005
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