  The subject of the present paper are stability properties of the solution set
to set-valued inclusions. The latter are problems emerging in robust
optimization and mathematical economics, which can not be cast in traditional
generalized equations. The analysis here reported focuses on several
quantitative forms of semicontinuity for set-valued mappings, widely
investigated in variational analysis, which include, among others, calmness.
Sufficient conditions for the occurrence of these properties in the case of the
solution mapping to a parameterized set-valued inclusion are established.
Consequences on the calmness of the optimal value function, in the context of
parametric optimization, are explored. Some specific tools for the analysis of
the sufficient conditions, in the case of set-valued inclusion with concave
data, are provided in a Banach space setting.
