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Strong Duality and Dual Pricing Properties in Semi-Infinite Linear Programming: A non-Fourier–Motzkin Elimination Approach

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  • Qinghong Zhang

    (Northern Michigan University)

Abstract

Following the idea of the conjecture for semi-infinite programming in a paper by Kortanek and Zhang, recently published in Optimization, in this paper we show that the Fourier–Motzkin elimination is not needed in the study of the strong duality and dual pricing properties for semi-infinite programming. We also prove several new results on the strong duality and dual pricing properties. Specifically, we propose a new subspace, under which the strong duality property holds. We give a necessary and sufficient condition for the dual pricing property to hold under this subspace, which is further used to examine the examples presented in the Basu–Martin–Ryan paper.

Suggested Citation

  • Qinghong Zhang, 2017. "Strong Duality and Dual Pricing Properties in Semi-Infinite Linear Programming: A non-Fourier–Motzkin Elimination Approach," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 702-717, December.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:3:d:10.1007_s10957-017-1184-2
    DOI: 10.1007/s10957-017-1184-2
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    References listed on IDEAS

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    1. A. Charnes & W. W. Cooper & K. Kortanek, 1965. "On Representations of Semi-Infinite Programs which Have No Duality Gaps," Management Science, INFORMS, vol. 12(1), pages 113-121, September.
    2. Goberna, M.A. & Gomez, S. & Guerra, F. & Todorov, M.I., 2007. "Sensitivity analysis in linear semi-infinite programming: Perturbing cost and right-hand-side coefficients," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1069-1085, September.
    3. A. Charnes & W. W. Cooper & K. Kortanek, 1963. "Duality in Semi-Infinite Programs and Some Works of Haar and Carathéodory," Management Science, INFORMS, vol. 9(2), pages 209-228, January.
    4. M. A. Goberna & T. Terlaky & M. I. Todorov, 2010. "Sensitivity Analysis in Linear Semi-Infinite Programming via Partitions," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 14-26, February.
    5. Amitabh Basu & Kipp Martin & Christopher Thomas Ryan, 2015. "Projection: A Unified Approach to Semi-Infinite Linear Programs and Duality in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 146-170, February.
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    Cited by:

    1. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.

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