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 tangential approximants most useful in nonsmooth analysis and optimization are those which lie "between" the Clarke tangent cone and the Bouligand contigent cone. A study of this class of tangent cones is undertaken here. It is shown that although no convex subcone of the contingent cone has the isotonicity property of the contingent cone, there are such convex subcones which are more "accurate" approximants than the Clarke tangent cone and possess an associated subdifferential calculus that is equally strong. In addition, a large class of convex subcones of the contingent cone can replace the Clarke tangent cone in necessary optimality conditions for a nonsmooth mathematical program. However, the Clarke tangent cone plays an essential role in the hypotheses under which these calculus rules and optimality conditions are proven. Overall, the results obtained here suggest that the most complete theory of nonsmooth analysis combines a number of different tangent cones.

Convex subcones of the contingent cone in nonsmooth calculus and optimization