Duality for Closed Convex Functions and Evenly Convex Functions
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We introduce two Moreau conjugacies for extended real-valued functions h on a separated locally convex space. In the first scheme, the biconjugate of h coincides with its closed convex hull, whereas, for the second scheme, the biconjugate of h is the evenly convex hull of h. In both cases, the biconjugate coincides with the supremum of the minorants of h that are either continuous affine or closed (respectively, open) halfspaces valley functions.
KeywordsMoreau conjugation Closed convex function Evenly convex function
The authors are grateful to the two anonymous referees and the editor for their constructive comments which have contributed to the final presentation of the paper. J.E. Martínez-Legaz has been supported by the MICINN of Spain, Grant MTM2011-29064-C03-01. He is affiliated to MOVE (Markets, Organizations and Votes in Economics). J. Vicente-Pérez has been supported by the MICINN of Spain, Grant MTM2011-29064-C03-02, and the Australian Research Council.
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