Fenchel's duality theorem for nearly convex functions

R. I. Boţ; S. M. Grad; G. Wanka

doi:10.1007/s10957-007-9234-9

Fenchel's duality theorem for nearly convex functions

R. I. Boţ
, S. M. Grad
, G. Wanka

Faculty of Mathematics
Fac. Math. of the TU

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

13 Citations (Scopus)

Résumé

We present an extension of Fenchel's duality theorem by weakening the convexity assumptions to near convexity. These weak hypotheses are automatically fulfilled in the convex case. Moreover, we show by a counterexample that a further extension to closely convex functions is not possible under these hypotheses.

langue originale	Anglais
Pages (de - à)	509-515
Nombre de pages	7
journal	Journal of Optimization Theory and Applications
Volume	132
Numéro de publication	3
Les DOIs	https://doi.org/10.1007/s10957-007-9234-9
état	Publié - 1 janv. 2007
Modification externe	Oui

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title = "Fenchel's duality theorem for nearly convex functions",

abstract = "We present an extension of Fenchel's duality theorem by weakening the convexity assumptions to near convexity. These weak hypotheses are automatically fulfilled in the convex case. Moreover, we show by a counterexample that a further extension to closely convex functions is not possible under these hypotheses.",

keywords = "Conjugate functions, Fenchel duality, Nearly convex functions",

author = "Bo{\c t}, \{R. I.\} and Grad, \{S. M.\} and G. Wanka",

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T1 - Fenchel's duality theorem for nearly convex functions

AU - Boţ, R. I.

AU - Grad, S. M.

AU - Wanka, G.

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N2 - We present an extension of Fenchel's duality theorem by weakening the convexity assumptions to near convexity. These weak hypotheses are automatically fulfilled in the convex case. Moreover, we show by a counterexample that a further extension to closely convex functions is not possible under these hypotheses.

AB - We present an extension of Fenchel's duality theorem by weakening the convexity assumptions to near convexity. These weak hypotheses are automatically fulfilled in the convex case. Moreover, we show by a counterexample that a further extension to closely convex functions is not possible under these hypotheses.

KW - Conjugate functions

KW - Fenchel duality

KW - Nearly convex functions

U2 - 10.1007/s10957-007-9234-9

DO - 10.1007/s10957-007-9234-9

M3 - Article

AN - SCOPUS:34547381810

SN - 0022-3239

VL - 132

SP - 509

EP - 515

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -

Fenchel's duality theorem for nearly convex functions

Résumé

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