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

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. Article Download View On the use of semi-closed sets and functions … Read more

On duality gap in linear conic problems

In their paper “Duality of linear conic problems” A. Shapiro and A. Nemirovski considered two possible properties (A) and (B) for dual linear conic problems (P) and (D). The property (A) is “If either (P) or (D) is feasible, then there is no duality gap between (P) and (D)”, while property (B) is “If both … Read more