Extensions of generalized differential calculus in Asplund spaces
The authors give an extended generalized differential calculus for nonconvex normal cones to sets, coderivatives of set-valued mappings and subdifferentials of extended real-valued functions in infinite-dimensional vector spaces, especially in Asplund spaces. Based on different versions of the extremal principle, a fuzzy intersection rule for the Fréchet normal cone and especially an intersection rule for the limiting normal cones to sets in product spaces (with respect to different topologies on the duals) are established. As a consequence one gets a representation of the limiting normal cones to inverse images of set-valued mappings. In the second part, these results are used for the derivation of sum rules and chain rules for the limiting coderivatives of set-valued mappings and for the limiting subdifferentials of real-valued functions.
scientific article; zbMATH DE number 1836783
scientific article