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Sufficiency and duality in interval-valued variational programming

Abstract

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.

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Acknowledgements

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.

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Correspondence to I. Ahmad.

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Ahmad, I., Jayswal, A., Al-Homidan, S. et al. Sufficiency and duality in interval-valued variational programming. Neural Comput & Applic 31, 4423–4433 (2019). https://doi.org/10.1007/s00521-017-3307-y

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  • DOI: https://doi.org/10.1007/s00521-017-3307-y

Keywords

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

Mathematical Subject Classification

  • 90C26
  • 90C30
  • 90C46