English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we introduce and study the concept of set extremality forsystems of convex sets in vector spaces without topological structures.Characterizations of the extremal systems of sets are obtained in the form ofthe convex extremal principle, which is shown to be equivalent to convexseparation under certain qualification conditions expressed via algebraiccores. The obtained results are applied via a variational geometric approach toderiving enhanced calculus rules for normals to convex sets, coderivatives ofconvex set-valued mappings, and subgradients of extended-real-valued convexfunctions including the optimal value ones. These rules of the equality typeare established under refined qualification conditions in terms of algebraiccores in arbitrary vector spaces. Our new developments partially answer thequestion on how far we can go with set-valued and convex analysis without anytopological structure on the underlying spaces.

Extremal Systems of Convex Sets with Applications to Convex Calculus in Vector Spaces