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...

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