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Duality Gap in Interval Linear Programming

Author

Listed:
  • Jana Novotná

    (Charles University)

  • Milan Hladík

    (Charles University)

  • Tomáš Masařík

    (Charles University)

Abstract

This paper deals with the problem of linear programming with inexact data represented by real intervals. We introduce the concept of duality gap to interval linear programming. We give characterizations of strongly and weakly zero duality gap in interval linear programming and its special case where the matrix of coefficients is real. We show computational complexity of testing weakly- and strongly zero duality gap for commonly used types of interval linear programming.

Suggested Citation

  • Jana Novotná & Milan Hladík & Tomáš Masařík, 2020. "Duality Gap in Interval Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 565-580, February.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:2:d:10.1007_s10957-019-01610-y
    DOI: 10.1007/s10957-019-01610-y
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    References listed on IDEAS

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    1. Elif Garajová & Milan Hladík & Miroslav Rada, 2019. "Interval linear programming under transformations: optimal solutions and optimal value range," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(3), pages 601-614, September.
    2. J W Chinneck & K Ramadan, 2000. "Linear programming with interval coefficients," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(2), pages 209-220, February.
    3. V Gabrel & C Murat, 2010. "Robustness and duality in linear programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1288-1296, August.
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