On interval valued functions and Mangasarian type duality involving Hukuhara derivative

Izhar Ahmad*, Deepak Singh, Bilal Ahmad Dar, S. Al-Homidan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper, we introduce twice weakly differentiable and twice H-diferentiable interval valued functions. The existence of twice H-differentiable interval-valued function and its relation with twice weakly differentiable functions are presented. Interval valued bonvex and generalized bonvex functions involving twice H-differentiability are proposed. Under the proposed settings, necessary conditions are elicited naturally in order to achieve LU-efficient solution. Mangasarian type dual is discussed for a nondifferentiable multiobjective programming problem and appropriate duality results are also derived. The theoretical developments are illustrated through non-trivial numerical examples.

Original languageEnglish
Pages (from-to)881-896
Number of pages16
JournalJournal of Computational Analysis and Applications
Issue number5
StatePublished - 2016

Bibliographical note

Funding Information:
The research of the first and fourth author is financially supported by King Fahd University of Petroleum and Minerals, Saudi Arabia under the Internal Research Project No. IN131026.

Publisher Copyright:
© 2016 by Eudoxus Press,LLC,All rights reserved.


  • Duality
  • Generalized bonvexity
  • Interval valued functions
  • LU-efficient solution
  • Twice H-differentiability
  • Twice weak differentiability

ASJC Scopus subject areas

  • Computational Mathematics


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