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Article Dans Une Revue Journal of Nonlinear and Convex Analysis Année : 2018

Envelopes for sets and functions II: generalized polarity and conjugacy

Résumé

Let X,Y be two nonempty sets, Φ an extended real-valued bivariate coupling function on X × Y and Γ a subset of X × Y. The present paper provides extensions to the well-known generalized Φ-conjugacy and Γ-polarity of diverse results of our previous work [2] related to φ-conjucacy and Λ-polarity, where Λ is a subset of a vector space E and φ is a function on E defining the particular coupling function (x,y)→φ(x−y) on E × E. A particular attention is devoted to the conjugacy functions (resp. polarity sets) which are mutually generating. Finally, for a superadditive conjugacy function Φ, we obtain a full description of the class of Φ-envelopes.
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Dates et versions

hal-01997447 , version 1 (29-01-2019)

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  • HAL Id : hal-01997447 , version 1

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Alexandre Cabot, Abderrahim Jourani, Lionel Thibault. Envelopes for sets and functions II: generalized polarity and conjugacy. Journal of Nonlinear and Convex Analysis, 2018, 19 (8), pp.1297-1318. ⟨hal-01997447⟩
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