Sufficiency and duality in interval-valued variational programming

I. Ahmad*, Anurag Jayswal, S. Al-Homidan, Jonaki Banerjee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


In the present paper, we focus our study on an interval-valued variational problem and derive sufficient optimality conditions by using the notion of invexity. In order to relate the primal interval-valued variational problem and its dual, several duality results, viz., weak, strong and converse duality results are established. Further, the Lagrangian function for the considered interval-valued variational problem is defined and we present some relations between an optimal solution of the considered interval-valued variational problem and a saddle point of the Lagrangian function. In order to illustrate the results proved in the paper, some examples of interval-valued variational problems have been formulated.

Original languageEnglish
Pages (from-to)4423-4433
Number of pages11
JournalNeural Computing and Applications
Issue number8
StatePublished - 1 Aug 2019

Bibliographical note

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

Publisher Copyright:
© 2018, The Natural Computing Applications Forum.


  • Duality
  • Interval-valued problem
  • Invexity
  • LU optimal
  • Sufficiency

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence


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