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Subdifferentials with respect to dualities

Authors:	Juan-Enrique Martinez-Legaz Ivan Singer

Institution:	(1) Dept. Economia i Historia Economica, Universitat Autonoma de Barcelona, Bellaterra, 08193 Barcelona, Spain;(2) Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania

Abstract:	LetX andW be two sets and: ¯R^X ¯R^W a duality (i.e., a mapping $\Delta :f \in \bar R^X \to f^\Delta \in \bar R^W$ such that $\left( {\mathop {\inf f_i }\limits_{i \in I} } \right)^\Delta = \mathop {\sup }\limits_{i \in I} f_i^\Delta$ for all $\{ f_i \} _{i \in I} \subseteq \bar R^X$ and all index setsI). We introduce and study the subdifferential $\partial ^\Delta f(x_0 )$ of a function $f \in \bar R^X$ at a pointx _o X, with respect to. We also consider the particular cases when is a (Fenchel-Moreau) conjugation, or a -duality, or a -duality, in the sense of 8].

Keywords:	Dualities generalized subdifferentials conjugations
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