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

Constantin Zalinescu(zalinesc***at***uaic.ro)

Abstract: The main aim of this short note is to show that the sub\-differentiability and duality results established by Laghdir (2005), Laghdir and Benabbou (2007), and Alimohammady \emph{et al.}\ (2011), stated in Fr├ęchet 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, sub\-differential, duality

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 04/11/2013
Entry Accepted: 04/11/2013
Entry Last Modified: 04/11/2013

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