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Wolfe Duality for Interval-Valued Optimization

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  • H. C. Wu

    (National Kaohsiung Normal University)

Abstract

Weak and strong duality theorems in interval-valued optimization problem based on the formulation of the Wolfe primal and dual problems are derived. The solution concepts of the primal and dual problems are based on the concept of nondominated solution employed in vector optimization problems. The concepts of no duality gap in the weak and strong sense are also introduced, and strong duality theorems in the weak and strong sense are then derived.

Suggested Citation

  • H. C. Wu, 2008. "Wolfe Duality for Interval-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 497-509, September.
    • Handle: RePEc:spr:joptap:v:138:y:2008:i:3:d:10.1007_s10957-008-9396-0
    DOI: 10.1007/s10957-008-9396-0
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    References listed on IDEAS

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    1. Soyster, A. L., 1979. "Inexact linear programming with generalized resource sets," European Journal of Operational Research, Elsevier, vol. 3(4), pages 316-321, July.
    2. 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.
    3. Wu, Hsien-Chung, 2007. "The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function," European Journal of Operational Research, Elsevier, vol. 176(1), pages 46-59, January.
    4. David J. Thuente, 1980. "Technical Note—Duality Theory for Generalized Linear Programs with Computational Methods," Operations Research, INFORMS, vol. 28(4), pages 1005-1011, August.
    5. James E. Falk, 1976. "Technical Note—Exact Solutions of Inexact Linear Programs," Operations Research, INFORMS, vol. 24(4), pages 783-787, August.
    6. 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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    Citations

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    Cited by:

    1. 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.
    2. Yating Guo & Guoju Ye & Wei Liu & Dafang Zhao & Savin Treanţǎ, 2021. "Optimality Conditions and Duality for a Class of Generalized Convex Interval-Valued Optimization Problems," Mathematics, MDPI, vol. 9(22), pages 1-14, November.
    3. 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.
    4. Khoirunnisa Rohadatul Aisy Muslihin & Endang Rusyaman & Diah Chaerani, 2022. "Conic Duality for Multi-Objective Robust Optimization Problem," Mathematics, MDPI, vol. 10(21), pages 1-22, October.
    5. 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.
    6. Guo, Yating & Ye, Guoju & Liu, Wei & Zhao, Dafang & Treanţă, Savin, 2022. "On symmetric gH-derivative: Applications to dual interval-valued optimization problems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    7. T. Antczak, 2018. "Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 205-224, January.

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