Delineating some nice classes of functions and sets JEAN-PAUL PENOT

During the last decades a number of concepts have been introduced to deal with non differentiable functions. Thus, one may get a feeling of disorder and be bewildered. Still, some classes of nonsmooth functions are of great interest in view of their stability properties and of the fact that their subdifferentials present some continuity or monotonicity properties. Such functions are characterized by some sorts of approximate convexity which form a full spectrum. Correspondingly, some classes of subsets can be delineated with similar features. We focus our attention on such favorable classes and on the correspondences between functions and sets which are one of the main features of nonsmooth analysis. Thus, some form of unity is emerging in nonsmooth analysis