Abstract
In the present paper, the problem of estimating the contingent cone
to the solution set associated with certain set-valued inclusions is addressed
by variational analysis methods and tools.
As a main result, inner (resp. outer) approximations, which are expressed
in terms of outer (resp. inner) prederivatives of the set-valued term
appearing in the inclusion problem, are provided. For the analysis of inner approximations,
the evidence arises that
the metric increase property for set-valued mappings turns out to play a crucial role.
Some of the results obtained in this context are then exploited for formulating
necessary optimality conditions for constrained problems, whose feasible region is defined by
a set-valued inclusion.