The main aim of this short note is to show that the subdifferentiability and duality results established by Laghdir (2005), Laghdir and Benabbou (2007), and Alimohammady et al. (2011), stated in Fréchet spaces, are consequences of the corresponding known results using Moreau-Rockafellar type conditions.
@article{bwmeta1.element.doi-10_1515_math-2015-0001,
author = {Constantin Z\u alinescu},
title = {On the use of semi-closed sets and functions in convex analysis},
journal = {Open Mathematics},
volume = {13},
year = {2015},
zbl = {1308.90132},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0001}
}
Constantin Zălinescu. On the use of semi-closed sets and functions in convex analysis. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0001/
[1] Alimohammady, M., Cho, Y.J., Dadashi, V., Roohi, M., Convex sub-differential sum rule via convex semi-closed functions with applications in convex programming, Appl. Math. Lett., 2011, 24(8), 1289-1294[Crossref] | Zbl 1219.26011
[2] Laghdir, M., Some remarks on subdifferentiability of convex functions, Appl. Math. E-Notes, 2005, 5, 150-156 (electronic) | Zbl 1085.49022
[3] Laghdir, M., Benabbou, R., Convex functions whose epigraphs are semi-closed: duality theory, Appl. Math. Sci. (Ruse), 2007, 1(21-24), 1019-1033 | Zbl 1200.90138
[4] Zălinescu, C., Convex Analysis in General Vector Spaces, World Scientific, River Edge, 2002 | Zbl 1023.46003
[5] Zălinescu, C., Hahn-Banach extension theorems for multifunctions revisited, Math. Methods Oper. Res., 2008, 68(3), 493-508[WoS] | Zbl 1171.90016