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Bi-parametric optimal partition invariancy sensitivity analysis in linear optimization


  • Alireza Ghaffari-Hadigheh


  • Habib Ghaffari-Hadigheh


  • Tamás Terlaky



In bi-parametric linear optimization (LO), perturbation occurs in both the right-hand-side and the objective function data with different parameters. In this paper, the bi-parametric LO problem is considered and we are interested in identifying the regions where the optimal partitions are invariant. These regions are referred to as invariancy regions. It is proved that invariancy regions are separated by vertical and horizontal lines and generate a mesh-like area. It is proved that the boundaries of these regions can be identified in polynomial time. The behavior of the optimal value function on these regions is investigated too. Copyright Springer-Verlag 2008

Suggested Citation

  • Alireza Ghaffari-Hadigheh & Habib Ghaffari-Hadigheh & Tamás Terlaky, 2008. "Bi-parametric optimal partition invariancy sensitivity analysis in linear optimization," 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. 16(2), pages 215-238, June.
  • Handle: RePEc:spr:cejnor:v:16:y:2008:i:2:p:215-238
    DOI: 10.1007/s10100-007-0054-7

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    Cited by:

    1. Yu-Ching Lee & Jong-Shi Pang & John Mitchell, 2015. "An algorithm for global solution to bi-parametric linear complementarity constrained linear programs," Journal of Global Optimization, Springer, vol. 62(2), pages 263-297, June.
    2. Hladík, Milan, 2010. "Multiparametric linear programming: Support set and optimal partition invariancy," European Journal of Operational Research, Elsevier, vol. 202(1), pages 25-31, April.


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