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Abstract
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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.
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