Maximal Abstract Monotonicity and Generalized Fenchel’s Conjugation Formulas

In this paper, we present a generalization of a theory of monotone operators in the framework of abstract convexity. We show that how generalized Fenchel’s conjugation formulas can be used to obtain some results on maximal abstract monotonicity. We give a necessary and sufficient condition for maxim...

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Bibliographic Details
Published in:	Set-Valued and Variational Analysis Vol. 18; no. 1; pp. 79 - 108
Main Authors:	Eberhard, A. C., Mohebi, Hossein
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01-03-2010
Subjects:	Analysis Mathematics Mathematics and Statistics Optimization Abstract convexity Abstract monotonicity 26A51 52A01 Generalized Fenchel’s duality Abstract convex function Monotone operator 26B25 47H05 47H04
Online Access:	Get full text
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Summary:	In this paper, we present a generalization of a theory of monotone operators in the framework of abstract convexity. We show that how generalized Fenchel’s conjugation formulas can be used to obtain some results on maximal abstract monotonicity. We give a necessary and sufficient condition for maximality of abstract monotone operators representable by abstract convex functions by using an additivity constraint qualification.
ISSN:	1877-0533 1572-932X 1877-0541
DOI:	10.1007/s11228-009-0124-1