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

Fac. Math. of the TU

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	509-515
Number of pages	7
Journal	Journal of Optimization Theory and Applications
Volume	132
Issue number	3
DOIs	https://doi.org/10.1007/s10957-007-9234-9
Publication status	Published - 1 Jan 2007
Externally published	Yes

Keywords

Conjugate functions
Fenchel duality
Nearly convex functions

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10.1007/s10957-007-9234-9

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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",

year = "2007",

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doi = "10.1007/s10957-007-9234-9",

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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

Abstract

Keywords

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