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Sufficient optimality conditions and duality theory for interval optimization problem

Author

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  • A. K. Bhurjee

    (Indian Institute of Technology Kharagpur)

  • G. Panda

    (Indian Institute of Technology Kharagpur)

Abstract

This paper addresses the duality theory of a nonlinear optimization model whose objective function and constraints are interval valued functions. Sufficient optimality conditions are obtained for the existence of an efficient solution. Three type dual problems are introduced. Relations between the primal and different dual problems are derived. These theoretical developments are illustrated through numerical example.

Suggested Citation

  • A. K. Bhurjee & G. Panda, 2016. "Sufficient optimality conditions and duality theory for interval optimization problem," Annals of Operations Research, Springer, vol. 243(1), pages 335-348, August.
    • Handle: RePEc:spr:annopr:v:243:y:2016:i:1:d:10.1007_s10479-014-1644-0
    DOI: 10.1007/s10479-014-1644-0
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    References listed on IDEAS

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    11. A. Bhurjee & G. Panda, 2012. "Efficient solution of interval optimization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 273-288, December.
    12. Wu, Hsien-Chung, 2009. "The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 49-60, July.
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    Cited by:

    1. Do Luu & Tran Thi Mai, 2018. "Optimality and duality in constrained interval-valued optimization," 4OR, Springer, vol. 16(3), pages 311-337, September.
    2. Muhammad Bilal Khan & Savin Treanțǎ & Mohamed S. Soliman & Kamsing Nonlaopon & Hatim Ghazi Zaini, 2022. "Some New Versions of Integral Inequalities for Left and Right Preinvex Functions in the Interval-Valued Settings," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    3. P. Kumar & A. K. Bhurjee, 2022. "Multi-objective enhanced interval optimization problem," Annals of Operations Research, Springer, vol. 311(2), pages 1035-1050, April.
    4. P. Kumar & G. Panda, 2017. "Solving nonlinear interval optimization problem using stochastic programming technique," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 752-765, December.

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