We show that in two dimensions or higher, the Mordukhovich-loffe approximate subdifferential and Clarke subdifferential may differ almost everywhere for real-valued Lipschitz functions. Uncountably many Frechet differentiable vector-valued Lipschitz functions differing by more than constants can share the same Mordukhovich-Ioffe coderivatives. Moreover, the approximate Jacobian associated with ...

The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the normal-cone mapping related to C2 inequality constraints under very weak qualification conditions. This enables us to provide the graphical derivative and the regular coderivative of the solution map to a class of parameterized generalized equations with the constraint set of the investi...

We obtain sufficient and/or necessary conditions for global/local error bounds for the distances to some sets appeared in set optimization studied with both the set approach and vector approach (sublevel sets, constraint sets, sets of all Pareto efficient/ Henig proper efficient/super efficient solutions, sets of solutions corresponding to one Pareto efficient/Henig proper efficient/super effic...

This paper is devoted to the development of new sufficient conditions for the calmness and the Aubin property of implicit multifunctions. As the basic tool we employ the directional limiting coderivative which, together with the graphical derivative, enables a fine analysis of the local behavior of the investigated multifunction along relevant directions. For verification of the calmness proper...

Due to proliferation of digital publishing, e-book catalogs are abundant but noisy and unstructured. Tools for the digital librarian rely on ISBN, metadata embedded into digital files (without accepted standard) and cryptographic hash functions for the identification of coderivative or nearduplicate content. However, unreliability of metadata and sensitivity of hashing to even smallest changes ...

The widespread use of on-line publishing of text promotes storage of multiple versions of documents and mirroring of documents in multiple locations, and greatly simplifies the task of plagiarizing the work of others. We evaluate two families of methods for searching a collection to find documents that are coderivative, that is, are versions or plagiarisms of each other. The first, the ranking ...

Thepaper ismainly devoted to the studyof implicitmultifunction theorems in terms of Fréchet coderivative inAsplund spaces. It sharpens thewell-known implicit multifunction theorem of Ledyaev and Zhu (Set Valued Anal., 7, 209–238, 1999) as well as many recent publications about this significant area.