Ghaffari-Hadigheh, Alireza; Mehanfar, Nayyer Matrix perturbation and optimal partition invariancy in linear optimization. (English) Zbl 1318.90069 Asia-Pac. J. Oper. Res. 32, No. 3, Article ID 1550013, 17 p. (2015). Summary: 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. Cited in 3 Documents MSC: 90C31 Sensitivity, stability, parametric optimization 90C05 Linear programming Keywords:optimal partition; linear parametric sensitivity analysis; Moore-Penrose inverse PDFBibTeX XMLCite \textit{A. Ghaffari-Hadigheh} and \textit{N. Mehanfar}, Asia-Pac. J. Oper. Res. 32, No. 3, Article ID 1550013, 17 p. (2015; Zbl 1318.90069) Full Text: DOI References: [1] DOI: 10.1007/978-3-0348-6293-6 · doi:10.1007/978-3-0348-6293-6 [2] DOI: 10.1016/0024-3795(92)90340-G · Zbl 0762.15003 · doi:10.1016/0024-3795(92)90340-G [3] DOI: 10.1016/0024-3795(90)90395-S · Zbl 0704.15005 · doi:10.1016/0024-3795(90)90395-S [4] DOI: 10.1016/0024-3795(86)90307-1 · Zbl 0562.15003 · doi:10.1016/0024-3795(86)90307-1 [5] DOI: 10.1007/978-3-642-88169-5 · doi:10.1007/978-3-642-88169-5 [6] Goldman A. J., Annals of Mathematical Studies 38, in: Linear Equalities and Related Systems (1956) [7] DOI: 10.1287/ijoc.11.3.316 · Zbl 0973.90049 · doi:10.1287/ijoc.11.3.316 [8] DOI: 10.1007/BF00933875 · Zbl 0298.90041 · doi:10.1007/BF00933875 [9] Roos C., Interior Point Algorithms for Linear Optimization (2005) [10] DOI: 10.1016/0377-2217(85)90116-X · Zbl 0577.90062 · doi:10.1016/0377-2217(85)90116-X This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.