On the use of semi-closed sets and functions in convex analysis
Open Mathematics (2015)
- Volume: 13, Issue: 1, page 1-5, electronic only
- ISSN: 2391-5455
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topConstantin Zălinescu. "On the use of semi-closed sets and functions in convex analysis." Open Mathematics 13.1 (2015): 1-5, electronic only. <http://eudml.org/doc/268879>.
@article{ConstantinZălinescu2015,
abstract = {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.},
author = {Constantin Zălinescu},
journal = {Open Mathematics},
keywords = {Semi-closed convex set; Semi-closed convex function; Semi-closure; Semi-interior; Subdifferential; Duality; semi-closed convex set; semi-closed convex function; semi-closure; semi-interior; subdifferential; duality},
language = {eng},
number = {1},
pages = {1-5, electronic only},
title = {On the use of semi-closed sets and functions in convex analysis},
url = {http://eudml.org/doc/268879},
volume = {13},
year = {2015},
}
TY - JOUR
AU - Constantin Zălinescu
TI - On the use of semi-closed sets and functions in convex analysis
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 1
EP - 5, electronic only
AB - 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.
LA - eng
KW - Semi-closed convex set; Semi-closed convex function; Semi-closure; Semi-interior; Subdifferential; Duality; semi-closed convex set; semi-closed convex function; semi-closure; semi-interior; subdifferential; duality
UR - http://eudml.org/doc/268879
ER -
References
top- [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] Zbl1219.26011
- [2] Laghdir, M., Some remarks on subdifferentiability of convex functions, Appl. Math. E-Notes, 2005, 5, 150-156 (electronic) Zbl1085.49022
- [3] Laghdir, M., Benabbou, R., Convex functions whose epigraphs are semi-closed: duality theory, Appl. Math. Sci. (Ruse), 2007, 1(21-24), 1019-1033 Zbl1200.90138
- [4] Zălinescu, C., Convex Analysis in General Vector Spaces, World Scientific, River Edge, 2002 Zbl1023.46003
- [5] Zălinescu, C., Hahn-Banach extension theorems for multifunctions revisited, Math. Methods Oper. Res., 2008, 68(3), 493-508[WoS] Zbl1171.90016
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