Bi-parametric matrix perturbation and optimal partition invariancy in linear optimization

In this paper, a linear programming problem with perturbation in the left-hand-side of constraints with two different parameters is considered. We are interested in identifying the boundary of a region at which the optimal partition is invariant. Here, this region is considered in twocategories as degenerate and nondegenerate invariancy regions which, respectively, are of dimensions less than 2, and 2. For each category a method is proposed. Two examples are provided to describe each method.

Keywords:

Matrix parametric linear optimization , Optimal partition invariancy , Moore-Penrose inverse , Singular value decomposition