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On Sensitivity in Linear Multiobjective Programming

Author

Listed:
  • L. V. Thuan

    (Hanoi Institute of Mathematics)

  • D. T. Luc

    (University of Avignon
    Hanoi Institute of Mathematics)

Abstract

In this paper, we prove that, if the data of a linear multiobjectiveprogramming problem are smooth functions of a parameter, then in theparameter space there is an open dense subset where the efficient solutionset of the problem can be locally represented as a union of some faces whosevertices and directions are smooth functions of the parameter.

Suggested Citation

  • L. V. Thuan & D. T. Luc, 2000. "On Sensitivity in Linear Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 615-626, December.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:3:d:10.1023_a:1026455401079
    DOI: 10.1023/A:1026455401079
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    References listed on IDEAS

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    1. J. V. Outrata, 1990. "On Generalized Gradients in Optimization Problems with Set-Valued Constraints," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 626-639, November.
    2. Stephen M. Robinson, 1991. "An Implicit-Function Theorem for a Class of Nonsmooth Functions," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 292-309, May.
    3. Hedy Attouch & Hassan Riahi, 1993. "Stability Results for Ekeland's ε-Variational Principle and Cone Extremal Solutions," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 173-201, February.
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    Cited by:

    1. Xi Yin Zheng & Xiaoqi Yang, 2021. "Fully Piecewise Linear Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 461-490, August.
    2. Pubudu L. W. Jayasekara & Andrew C. Pangia & Margaret M. Wiecek, 2023. "On solving parametric multiobjective quadratic programs with parameters in general locations," Annals of Operations Research, Springer, vol. 320(1), pages 123-172, January.

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