Stability Theory for Systems of Inequalities. Part I: Linear Systems

Abstract

This paper deals with the stability of systems of linear inequalities in partially ordered Banach spaces when the data are subjected to small perturbations. We show that a certain condition is necessary and sufficient for such stability. For some of the more important special cases, this condition is computationally verifiable; it reduces to the classical full-row-rank condition in the case of equations alone. In addition, we give quantitative estimates for the magnitudes of the changes in the solution sets in terms of the magnitudes of the perturbations.