On tangential approximations of the solution set of set-valued inclusions

Abstract In the present paper, problem of estimating contingent cone to 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 outer inner) prederivatives term appearing inclusion problem, provided. For evidence arises that metric increase property for mappings turns out play crucial role. Some results obtained this context then exploited formulating necessary optimality conditions constrained problems, whose feasible region defined inclusion.