Sufficiency and Duality for Nonsmooth Interval-Valued Optimization Problems via Generalized Invex-Infine Functions

Izhar Ahmad, Krishna Kummari*, S. Al-Homidan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper, a new concept of generalized-affineness type of functions is introduced. This class of functions is more general than some of the corresponding ones discussed in Chuong (Nonlinear Anal Theory Methods Appl 75:5044–5052, 2018), Sach et al. (J Global Optim 27:51–81, 2003) and Nobakhtian (Comput Math Appl 51:1385–1394, 2006). These concepts are used to discuss the sufficient optimality conditions for the interval-valued programming problem in terms of the limiting/Mordukhovich subdifferential of locally Lipschitz functions. Furthermore, two types of dual problems, namely Mond–Weir type and mixed type duals are formulated for an interval-valued programming problem and usual duality theorems are derived. Our results improve and generalize the results appeared in Kummari and Ahmad (UPB Sci Bull Ser A 82(1):45–54, 2020).

Original languageEnglish
Pages (from-to)505-527
Number of pages23
JournalJournal of the Operations Research Society of China
Issue number3
StatePublished - Sep 2023

Bibliographical note

Funding Information:
The authors are highly thankful to anonymous referees for their valuable suggestions/comments that helped to improve this article in its present form.

Publisher Copyright:
© 2022, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature.


  • Constraint qualifications
  • Duality
  • Generalized invex-infine function
  • Interval-valued programming
  • LU-optimal
  • Locally Lipschitz functions
  • Mordukhovich subdifferential

ASJC Scopus subject areas

  • Mathematics (all)
  • Management Science and Operations Research


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