Robust global error bounds for uncertain linear inequality systems with applications

Abstract

In this paper, we examine global error bounds for a linear inequality system in the face of data uncertainty by building upon recent developments in robust optimization, where the uncertain parameters are assumed to be in prescribed uncertainty sets. We present necessary and sufficient dual conditions for the existence of robust global error bounds. As a consequence, we obtain a robust Hoffman error bound in the case of commonly used interval data uncertainty, extending the well-known Hoffman's error bound. We then introduce the notion of radius of robust global error bound under interval data uncertainty and present a formula for finding the radius by examining the stability of robust global error bounds. It provides the radius of the largest interval uncertainty set in which the uncertain system admits a robust global error bound. As an immediate application to robust linear programming, we provide conditions for robust feasibility and give a formula for radius of robust feasibility of an uncertain linear program.