We consider the classical duality operators for convex objects suchas the polar of a convex set containing the origin, the dual norm,the Fenchel-transform of a convex function and the conjugate of aconvex cone. We give a new, sharper, unified treatment of the theoryof these operators, deriving...

Our aim is to give a simple view on the basics and applications of convex analysis. The essential feature of this account is the systematic use of the possibility to associate to each convex object---such as a convex set, a convex function or a convex extremal problem--- a cone, without loss of...

We consider the classical duality operators for convex objects such as the polar of a convex set containing the origin, the dual norm, the Fenchel-transform of a convex function and the conjugate of a convex cone. We give a new, sharper, unified treatment of the theory of these operators,...

Our aim is to give a simple view on the basics and applications of convex analysis. The essential feature of this account is the systematic use of the possibility to associate to each convex object---such as a convex set, a convex function or a convex extremal problem--- a cone, without loss of...

We consider the classical duality operators for convex objects such as the polar of a convex set containing the origin, the dual norm, the Fenchel-transform of a convex function and the conjugate of a convex cone. We give a new, sharper, unified treatment of the theory of these operators,...

The following four questions could be asked about each extremalproblem:1. What are the conditions for an extremum of theproblem (necessary, sufficient, necessary andsufficient)?2. How to describe the evolution of sulutions if theproblem is perturbed?3. Does a solution to the problem exist or...