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

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,...