  In the present paper, some aspects of the finite-dimensional theory of
set-inclusive generalized equations are studied. Set-inclusive generalized
equations are problems arising in several contexts of optimization and
variational analysis, involving multi-valued mappings and cones. The aim of
this paper is to propose an approach to the local analysis of the solution set
to such kind of generalized equations. In particular, a study of the contingent
cone to the solution set is carry out by means of first-order approximations of
set-valued mappings, which are expressed by prederivatives. Such an approach
emphasizes the role of the metric increase property for set-valued mappings, as
a condition triggering crucial error bound estimates for the tangential
description of solution sets. Some of the results obtained through this kind of
analysis are then exploited for formulating necessary optimality conditions,
which are valid for problems with constraints formalized by set-inclusive
generalized equations.
