Enlargements of the Moreau–Rockafellar Subdifferential

Subdifferential enlargements and continuity properties of the VU -decomposition in convex optimization

We review the concept of VU-decomposition of nonsmooth convex functions, which is closely related to the notion of partly smooth functions. As VU-decomposition depends on the subdifferential at the given point, the associated objects lack suitable continuity properties (because the subdifferential lacks them), which poses an additional challenge to the already difficult task of constructing sup...

Enlargements of Filtrations

Enlargements of Categories

In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorical properties are well behaved under enlargements.

Enlargements of positive sets

Article history: Received 27 November 2008 Available online 11 March 2009 Submitted by A. Dontchev

Enlargements of schemes

In this article we use our previous constructions (L. Brünjes, C. Serpé, Theory Appl. Categ. 14:357–398, 2005) to lay down some foundations for the application of A. Robinson’s nonstandard methods to modern algebraic geometry. The main motivation is the search for another tool to transfer results from characteristic zero to positive characteristic and vice versa. We give applications to the res...