On the use of semi-closed sets and functions in convex analysis

• Autorzy: Constantin Zălinescu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Semi-closed convex set; Semi-closed convex function; Semi-closure; Semi-interior; Subdifferential; Duality

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

wydano

2015-01-01

otrzymano

2013-08-24

zaakceptowano

2014-03-19

online

2014-10-09

Twórcy

autor

Constantin Zălinescu

• Faculty of Mathematics, University Alexandru Ioan Cuza, Iaşi, Romania/ Octav Mayer Institute of Mathematics, Romanian Academy, Iaşi, Romania

Bibliografia

• [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]
• [2] Laghdir, M., Some remarks on subdifferentiability of convex functions, Appl. Math. E-Notes, 2005, 5, 150-156 (electronic)
• [3] Laghdir, M., Benabbou, R., Convex functions whose epigraphs are semi-closed: duality theory, Appl. Math. Sci. (Ruse), 2007, 1(21-24), 1019-1033
• [4] Zălinescu, C., Convex Analysis in General Vector Spaces, World Scientific, River Edge, 2002
• [5] Zălinescu, C., Hahn-Banach extension theorems for multifunctions revisited, Math. Methods Oper. Res., 2008, 68(3), 493-508[WoS]

Identyfikatory

DOI

10.1515/math-2015-0001