Publicación:
Fenchel-Moreau conjugation for lower semi-continuous functions
Fenchel-Moreau conjugation for lower semi-continuous functions
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Fecha
2011
Autores
Cotrina J.
Karas E.W.
Ribeiro A.A.
Sosa W.
Yuan J.Y.
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Editor
Taylor & Francis
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Abstracto
We introduce a modification of Fenchel's conjugation which is a particular case of Moreau's conjugation. We obtain good properties such as convexity of the conjugate function even though the function is not convex. We also introduce the concept of conjugate dual space as a class of continuous operators, while in the Fenchel conjugation the conjugate dual space is the classical topological dual space. Finally, we present some examples for illustrating the difference between the Fenchel–Moreau conjugation and our modification.
Descripción
The authors would like to thank Prof. Alfredo N. Iusem for useful discussions about the subject. We thank Juan-Enrique Martı´nez-Legaz, Tyrrell Rockafellar, Alberto Seeger and Benar Svaiter for their valuable comments. We also thank Juan-Enrique Martı´nez-Legaz for sending us the references [4,7–10]. W. Sosa likes to thank Prof. Carlos Henrique dos Santos and Prof. Raul Prado for their kindest hospitality during his visiting at Department of Mathematics, Federal University of Parana´, Curitiba, Brazil. This work was partially supported by PRONEX – Optimization, CNPq, CAPES, Fundac¸a˜o Arauca´ria, Brazil and CONCYTEC (projects STIC-AMSUD), Peru.
Palabras clave
proper function,
Fenchel–Moreau conjugate