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Sufficiency and duality in interval-valued variational programming

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    I. Ahmad & S. Al-Homidan

  2. Department of Applied Mathematics, Indian School of Mines, Dhanbad, Jharkhand, 826004, India

    Anurag Jayswal & Jonaki Banerjee

Authors
  1. I. Ahmad
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  2. Anurag Jayswal
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  3. S. Al-Homidan
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  4. Jonaki Banerjee
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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

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