Duality for Closed Convex Functions and Evenly Convex Functions

M. Volle (), Juan Enrique Martinez-Legaz and J. Vicente-Pérez ()
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M. Volle: Avignon University
J. Vicente-Pérez: University of New South Wales

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 3, No 14, 985-997

Abstract: Abstract 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.

Keywords: Moreau conjugation; Closed convex function; Evenly convex function (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-013-0395-4

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