Constantin Zalinescu

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

  • Constantin Zalinescu
    • Categories Convex Optimization Tags , , , , ,

    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 Fréchet 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

  • Constantin Zalinescu
    • Categories Linear, Cone and Semidefinite Programming Tags ,

    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