Strong and total Fenchel dualities for robust convex optimization problems

Abstract

In this paper, we present some strong and total Fenchel dualities for convex programming problems with data uncertainty within the framework of robust optimization in locally convex Hausdorff vector spaces. By using the properties of the epigraph of the conjugate functions, we give some new constraint qualifications, which characterizes completely the strong duality and the stable strong duality. Moreover, some sufficient and/or necessary conditions for the total duality and converse duality are also obtained.