Lipschitz behaviour of the Legendre-Fenchel transform (Q1332533)
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scientific article; zbMATH DE number 627462
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lipschitz behaviour of the Legendre-Fenchel transform |
scientific article; zbMATH DE number 627462 |
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Lipschitz behaviour of the Legendre-Fenchel transform (English)
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31 August 1994
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An estimate of the modulus of continuity of the Legendre-Fenchel transform, acting on the set of extended real-valued convex functions, is given. The functions are defined on a normed vector space or on its dual space equipped with the Attouch-Wets topology. It is proved further that the Legendre-Fenchel transform has a locally Lipschitz behaviour when the set of closed proper convex functions is endowed with suitable families of semimetrics.
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normed vector space
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Attouch-Wets topology
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Legendre-Fenchel transform
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