Résumé
Etant donné un opérateur de fermeture on s'intéresse aux fonctions réelles dont les tranches sont fermées. Ces fonctions, stables par passage à l'enveloppe supérieure, définissent une régularisation. En décomposant l'opérateur de fermeture relativement à une polarité, on introduit une (bi) conjugaison des fonctions réelles f de sorte que la biconjuguée de f coïncide avec sa régularisée. La théorie s'applique à diverses formes de dualité quasiconvexe et à la programmation mathématique en général.
Summary
We are interested here by 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.
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Je tiens à remercier le referee dont j'ai beaucoup apprécié la critique constructive.
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Volle, M. Conjugaison par tranches. Annali di Matematica Pura ed applicata 139, 279–311 (1985). https://doi.org/10.1007/BF01766858
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DOI: https://doi.org/10.1007/BF01766858