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Duality Theory for Optimization Problems with Interval-Valued Objective Functions

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  • H. C. Wu

    (National Kaohsiung Normal University)

Abstract

A solution concept in optimization problems with interval-valued objective functions, which is essentially similar to the concept of nondominated solution in vector optimization problems, is introduced by imposing a partial ordering on the set of all closed intervals. The interval-valued Lagrangian function and interval-valued Lagrangian dual function are also proposed to formulate the dual problem of the interval-valued optimization problem. Under this setting, weak and strong duality theorems can be obtained.

Suggested Citation

  • H. C. Wu, 2010. "Duality Theory for Optimization Problems with Interval-Valued Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 615-628, March.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:3:d:10.1007_s10957-009-9613-5
    DOI: 10.1007/s10957-009-9613-5
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    References listed on IDEAS

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    1. A. L. Soyster, 1974. "Technical Note—A Duality Theory for Convex Programming with Set-Inclusive Constraints," Operations Research, INFORMS, vol. 22(4), pages 892-898, August.
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    4. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    5. James E. Falk, 1976. "Technical Note—Exact Solutions of Inexact Linear Programs," Operations Research, INFORMS, vol. 24(4), pages 783-787, August.
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    Cited by:

    1. Hsien-Chung Wu, 2011. "Duality Theory in Interval-Valued Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 298-316, August.
    2. Hsien-Chung Wu, 2019. "Applying the concept of null set to solve the fuzzy optimization problems," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 279-314, September.
    3. 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.
    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.
    5. G. S. Mahapatra & T. K. Mandal, 2012. "Posynomial Parametric Geometric Programming with Interval Valued Coefficient," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 120-132, July.
    6. B. Japamala Rani & Krishna Kummari, 2023. "Duality for fractional interval-valued optimization problem via convexificator," OPSEARCH, Springer;Operational Research Society of India, vol. 60(1), pages 481-500, March.

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