We are concerned with contingent derivatives and their second-order counterparts (introduced by Ngai et al.) of set-valued mappings. Special attention is given to the development of new sum-rules for second-order contingent derivatives. To be precise, we want to find conditions under which the second-order contingent derivative of the sum of a smooth and a set-valued … Read more
It is known that second-order (Studniarski) contingent derivatives can be used to compute tangents to the solution set of a generalized equation when standard (first-order) regularity conditions are absent, but relaxed (second-order) regularity conditions are fulfilled. This fact, roughly speaking, is only relevant in practice as long as the computation of second-order contingent derivatives itself … Read more
We study the boundary structure of closed convex cones, with a focus on facially dual complete (nice) cones. These cones form a proper subset of facially exposed convex cones, and they behave well in the context of duality theory for convex optimization. Using the well-known and very commonly used concept of tangent cones in nonlinear … Read more
This paper considers computation of Fr\’echet and limiting normal cones to a finite union of polyhedra. To this aim, we introduce a new concept of normally admissible stratification which is convenient for calculations of such cones and provide its basic properties. We further derive formulas for the above mentioned cones and compare our approach to … Read more