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Efficient solution of interval optimization problem

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  • A. Bhurjee
  • G. Panda

Abstract

In this paper the interval valued function is defined in the parametric form and its properties are studied. A methodology is developed to study the existence of the solution of a general interval optimization problem, which is expressed in terms of the interval valued functions. The methodology is applied to the interval valued convex quadratic programming problem. Copyright Springer-Verlag 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:76:y:2012:i:3:p:273-288
    DOI: 10.1007/s00186-012-0399-0
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    References listed on IDEAS

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    1. Ishibuchi, Hisao & Tanaka, Hideo, 1990. "Multiobjective programming in optimization of the interval objective function," European Journal of Operational Research, Elsevier, vol. 48(2), pages 219-225, September.
    2. Jiang, C. & Han, X. & Liu, G.R. & Liu, G.P., 2008. "A nonlinear interval number programming method for uncertain optimization problems," European Journal of Operational Research, Elsevier, vol. 188(1), pages 1-13, July.
    3. V. Jeyakumar & G. Y. Li, 2011. "Robust Duality for Fractional Programming Problems with Constraint-Wise Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 292-303, November.
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    Citations

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    Cited by:

    1. P. Kumar & A. K. Bhurjee, 2022. "Multi-objective enhanced interval optimization problem," Annals of Operations Research, Springer, vol. 311(2), pages 1035-1050, April.
    2. 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.
    3. Ajay Kumar Bhurjee, 2016. "Existence of Equilibrium Points for Bimatrix Game with Interval Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-13, March.
    4. Aihong Ren & Yuping Wang, 2014. "A cutting plane method for bilevel linear programming with interval coefficients," Annals of Operations Research, Springer, vol. 223(1), pages 355-378, December.
    5. P. Kumar & Jyotirmayee Behera & A. K. Bhurjee, 2022. "Solving mean-VaR portfolio selection model with interval-typed random parameter using interval analysis," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 41-77, March.
    6. Lifeng Li, 2023. "Optimality conditions for nonlinear optimization problems with interval-valued objective function in admissible orders," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 247-265, June.
    7. Ajay Kumar Bhurjee & Geetanjali Panda, 2017. "Optimal strategies for two-person normalized matrix game with variable payoffs," Operational Research, Springer, vol. 17(2), pages 547-562, July.
    8. Omid Solaymani Fard & Mohadeseh Ramezanzadeh, 2017. "On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach," Complexity, Hindawi, vol. 2017, pages 1-12, September.
    9. 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.
    10. Mrinal Jana & Geetanjali Panda, 2018. "$$\chi$$ χ -Optimal solution of single objective nonlinear optimization problem with uncertain parameters," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 165-186, March.
    11. Fang-Xuan Hong & Deng-Feng Li, 2017. "Nonlinear programming method for interval-valued n-person cooperative games," Operational Research, Springer, vol. 17(2), pages 479-497, July.
    12. 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.
    13. Debdas Ghosh, 2016. "A Newton method for capturing efficient solutions of interval optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 648-665, September.
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    15. Ali Sadeghi & Mansour Saraj & Nezam Mahdavi Amiri, 2018. "Efficient Solutions of Interval Programming Problems with Inexact Parameters and Second Order Cone Constraints," Mathematics, MDPI, vol. 6(11), pages 1-13, November.

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