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 article, we study the notion of gH-Hadamard derivative forinterval-valued functions (IVFs) and its applications to interval optimizationproblems (IOPs). It is shown that the existence of gH-Hadamard derivativeimplies the existence of gH-Frechet derivative and vise-versa. Further, it isproved that the existence of gH-Hadamard derivative implies the existence ofgH-continuity of IVFs. We found that the composition of a Hadamarddifferentiable real-valued function and a gH-Hadamard differentiable IVF isgHHadamard differentiable. Further, for finite comparable IVF, we prove thatthe gH-Hadamard derivative of the maximum of all finite comparable IVFs is themaximum of their gH-Hadamard derivative. The proposed derivative is observed tobe useful to check the convexity of an IVF and to characterize efficient pointsof an optimization problem with IVF. For a convex IVF, we prove that if at apoint the gH-Hadamard derivative does not dominate to zero, then the point isan efficient point. Further, it is proved that at an efficient point, thegH-Hadamard derivative does not dominate zero and also contains zero. Forconstraint IOPs, we prove an extended Karush-Kuhn-Tucker condition by using theproposed derivative. The entire study is supported by suitable examples.

Generalized Hukuhara Hadamard Derivative of Interval-valued Functions and Its Applications to Interval Optimization