Bot, Radu Ioan ; Grad, Sorin Mihai ; Wanka, Gert : Fenchel's duality theorem for nearly convex functions

Author(s):

Bot, Radu Ioan
Grad, Sorin Mihai
Wanka, Gert

Title:

Fenchel's duality theorem for nearly convex functions

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 13, 2005

Mathematics Subject Classification:

42A50			[ Conjugate functions, conjugate series, singular integrals ]
26A51			[ Convexity, generalizations ]
49N15			[ Duality theory ]

Abstract:

We present an extension of Fenchel's duality theorem to nearly convexity, giving weaker conditions under which it takes place. Instead of minimizing the difference between a convex and a concave function, we minimize the subtraction of a nearly concave function from a nearly convex one. The assertion in the special case of Fenchel's duality theorem that consists in minimizing the difference between a convex function and a concave function pre-composed with a linear transformation is also proven to remain valid when one considers nearly convexity. We deliver an example where the Fenchel's classical duality theorem is not applicable, unlike the extension we have introduced, and an application related to games theory.

Keywords:

conjugate functions, nearly convex functions, Fenchel duality

Language:

English

Publication time:

9 / 2005