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Conjugaison par tranches. (French) Zbl 0581.49007

We are interested here in extended real-valued functions whose level sets are closed with respect to a given closure operator. This class of functions is closed under pointwise suprema so that a regularization can be defined. By using the notion of polarity we decompose the closure operator and introduce a (bi) conjugation for the real extended valued functions f such that the biconjugate of f is just the regularized of f. We apply this theory to many forms of quasiconvex dualities and to mathematical programming in the general form.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
49N15 Duality theory (optimization)
90C25 Convex programming
06A15 Galois correspondences, closure operators (in relation to ordered sets)
06B23 Complete lattices, completions
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