Matrix perturbation and Optimal Partition invariancy in Linear Optimization

Thought, knowing the effect of variation of the coefficient matrix in linear optimization problem on optimal solution and optimal value function has its own importance in practice; there are few published results in this area. Most of them are on the effect of this variation when the current optimal solution is a basic one. There is only a study of the problem when the given optimal solution is strictly complementary and the optimal partition is known. However, that study only includes special perturbation on the matrix. Here, we consider an arbitrary direction matrix and present an effective method based on generalized inverse and singular values to detect invariancy interval and corresponding transition points.