Matrix Perturbation and Optimal Partition Invariancy in Linear Optimization

Alireza Ghaffari-Hadigheh () and Nayyer Mehanfar ()
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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

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 03, 1-17

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.

Keywords: Optimal partition; linear parametric sensitivity analysis; Moore–Penrose inverse (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S021759591550013X

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