Fenchel-Moreau conjugation for lower semi-continuous functions

Abstract

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.Consejo Nacional de Ciencia, Tecnología e Innovación Tecnológica - Concyte