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Matrix Perturbation and Optimal Partition Invariancy in Linear Optimization

Author

Listed:
  • Alireza Ghaffari-Hadigheh

    (Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran)

  • Nayyer Mehanfar

    (Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran)

Abstract

Understanding the effect of variation of the coefficient matrix in linear optimization problem on the optimal solution and the optimal value function has its own importance in practice. However, most of the published results are on the effect of this variation when the current optimal solution is a basic one. There is only a study of the problem for special perturbation on the coefficient matrix, when the given optimal solution is strictly complementary and the optimal partition (in some sense) is known. Here, we consider an arbitrary direction for perturbation of the coefficient matrix and present an effective method based on generalized inverse and singular values to detect invariancy intervals and corresponding transition points.

Suggested Citation

  • Alireza Ghaffari-Hadigheh & Nayyer Mehanfar, 2015. "Matrix Perturbation and Optimal Partition Invariancy in Linear Optimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-17.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:03:n:s021759591550013x
    DOI: 10.1142/S021759591550013X
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    References listed on IDEAS

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    1. Zuidwijk, R.A., 2005. "Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs," ERIM Report Series Research in Management ERS-2005-055-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
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