TY - JOUR
T1 - Duality for Closed Convex Functions and Evenly Convex Functions
AU - Volle, M.
AU - Martínez-Legaz, J. E.
AU - Vicente-Pérez, J.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - © 2013, Springer Science+Business Media New York. 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.
AB - © 2013, Springer Science+Business Media New York. 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.
KW - Closed convex function
KW - Evenly convex function
KW - Moreau conjugation
U2 - 10.1007/s10957-013-0395-4
DO - 10.1007/s10957-013-0395-4
M3 - Article
SN - 0022-3239
VL - 167
SP - 985
EP - 997
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 3
ER -