Subdifferential of composition of sets and of mappings (Q796046)

The aim of this paper is to give some formulas for subdifferentials (conical approximations) of the compositions of sets and functions by using the definition of the finite systems of cones in a topological vector space to be in general position. Next some notations of the regularised cones to a given set in a given point are introduced. Some properties of these cones constructed for the Cartesian product of two sets and for the image of a set under a linear operator are presented. The regularity of these cones is studied. By using these results some properties of the subgradients of the composition of two functions are obtained. The main result of this paper says that the normal cone of the composition of two sets is contained in the composition of the normal cones to these sets.