On the Rate of Change in the Solution Set of a Perturbed Linear Program.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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The paper finds bounds for the displacement in the solution set of a system of linear inequalities caused by perturbations in the coefficient matrix andor the right-hand side, and these are applied to estimate the error in the optimal variables of a perturbed linear program. The main result is that if a superconsistent linear program is subjected to a sequence of perturbations approaching zero, for which a uniformly bounded sequence of primal solutions to the perturbed programs exists, then the distances from those solutions to the solution set of the unperturbed program are of the large order of the perturbations. Author
- Operations Research