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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 9, 2014

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

  • Constantin Zălinescu EMAIL logo
From the journal Open Mathematics

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.

References

[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), 1289-129410.1016/j.aml.2011.01.046Search in Google Scholar

[2] Laghdir, M., Some remarks on subdifferentiability of convex functions, Appl. Math. E-Notes, 2005, 5, 150-156 (electronic)Search in Google Scholar

[3] Laghdir, M., Benabbou, R., Convex functions whose epigraphs are semi-closed: duality theory, Appl. Math. Sci. (Ruse), 2007, 1(21-24), 1019-1033Search in Google Scholar

[4] Zălinescu, C., Convex Analysis in General Vector Spaces, World Scientific, River Edge, 200210.1142/5021Search in Google Scholar

[5] Zălinescu, C., Hahn-Banach extension theorems for multifunctions revisited, Math. Methods Oper. Res., 2008, 68(3), 493-50810.1007/s00186-007-0193-6Search in Google Scholar

Received: 2013-8-24
Accepted: 2014-3-19
Published Online: 2014-10-9
Published in Print: 2015-1-1

© 2015 Constantin Zălinescu

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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