Bi-parametric optimal partition invariancy sensitivity analysis in linear optimization

  • Alireza Ghaffari-Hadigheh
  • Habib Ghaffari-Hadigheh
  • Tamás Terlaky
Original Paper


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.


Linear optimization Bi-parametric sensitivity analysis Optimal partition Invariancy region Optimal value function 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Alireza Ghaffari-Hadigheh
    • 1
  • Habib Ghaffari-Hadigheh
    • 2
  • Tamás Terlaky
    • 3
  1. 1.Department of MathematicsAzarbaijan University of Tarbiat MoallemTabrizIran
  2. 2.Department of MathematicsPayame noor UniversityShabestarIran
  3. 3.School of Computational Engineering and Science, Department of Computing and SoftwareMcMaster UniversityHamiltonCanada

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