Solution analysis for a class of set-inclusive generalized equations: a convex analysis approach

Abstract

In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the case the set-valued term appearing in the generalized equation is concave. A functional characterization of the contingent cone to the solution set is provided via directional derivatives. Specializations of these results are also considered when outer prederivatives can be employed.