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Technical Note—Duality Theory for Generalized Linear Programs with Computational Methods

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  • David J. Thuente

    (Indiana University-Purdue University, Fort Wayne, Indiana)

Abstract

This paper presents a duality theory for generalized linear programs which parallels the usual duality results for linear programming. The duals are a form of inexact linear programs and can be solved by the simplex method. Computational methods with examples and applications are given.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:4:p:1005-1011
    DOI: 10.1287/opre.28.4.1005
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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. Robin Vujanic & Paul Goulart & Manfred Morari, 2016. "Robust Optimization of Schedules Affected by Uncertain Events," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 1033-1054, December.
    3. Soyster, A.L. & Murphy, F.H., 2017. "Data driven matrix uncertainty for robust linear programming," Omega, Elsevier, vol. 70(C), pages 43-57.
    4. Gorissen, B.L., 2014. "Practical robust optimization techniques and improved inverse planning of HDR brachytherapy," Other publications TiSEM 931e020a-2486-4e12-9731-3, Tilburg University, School of Economics and Management.
    5. 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.
    6. Soyster, A.L. & Murphy, F.H., 2013. "A unifying framework for duality and modeling in robust linear programs," Omega, Elsevier, vol. 41(6), pages 984-997.
    7. 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.
    8. Gorissen, B.L. & Ben-Tal, A. & Blanc, J.P.C. & den Hertog, D., 2012. "A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets," Other publications TiSEM e4c05682-e13c-4d1a-bc3f-a, Tilburg University, School of Economics and Management.
    9. H. C. Wu, 2008. "Wolfe Duality for Interval-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 497-509, September.
    10. 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.
    11. Jaroslav Ramík & Milan Vlach, 2016. "Intuitionistic fuzzy linear programming and duality: a level sets approach," Fuzzy Optimization and Decision Making, Springer, vol. 15(4), pages 457-489, December.
    12. Bram L. Gorissen & Hans Blanc & Dick den Hertog & Aharon Ben-Tal, 2014. "Technical Note---Deriving Robust and Globalized Robust Solutions of Uncertain Linear Programs with General Convex Uncertainty Sets," Operations Research, INFORMS, vol. 62(3), pages 672-679, June.

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