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

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.

Keywords

• semi-closed convex set
• semi-closed convex function
• semi-closure
• semi-interior
• subdifferential
• duality