Stability of linear inequality systems measured by the Hausdorff metric (Q5926375)

The authors propose a Hausdorff metric to measure the ``distance'' between two linear inequality systems on a real normed space \(X\). For this topology, which comes through a pseudo-metric in the set \(\Sigma\) of linear inequality systems, the closedness of the feasible set mapping is studied, and at the same time a characterization of the stability of the subset \(\Sigma_C\) of consistent system is given.