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

The support of a vector in R d is the set of indices with nonzero entries.Functions of the support have the property to be 0-homogeneous and, because ofthat, the Fenchel conjugacy fails to provide relevant analysis. In this paper,we define the coupling Capra between R d and itself by dividing the classicFenchel scalar product coupling by a given (source) norm on R d. Our mainresult is that, when both the source norm and its dual norm areorthant-strictly monotonic, any nondecreasing finite-valued function of thesupport mapping is Capra-convex, that is, is equal to its Capra-biconjugate(generalized convexity). We also establish that any such function is thecomposition of a proper convex lower semi continuous function on R d with thenormalization mapping on the unit sphere (hidden convexity), and that, whennormalized, it admits a variational formulation, which involves a family ofgeneralized local-K-support dual norms.

Constant Along Primal Rays Conjugacies and Generalized Convexity for Functions of the Support