On Robust Global Error Bounds for a Class of Uncertain Piecewise Linear Inequality Systems

Abstract

This paper is concerned with the radius of robust global error bounds for an uncertain piecewise linear inequality system where the uncertain data are assumed to be in polytope uncertain sets. We first present a dual characterization for robust global error bounds of this uncertain piecewise linear inequality system. Then, we establish upper and lower bounds for the radius of robust global error bounds of the system of uncertain piecewise linear inequalities in terms of the Minkowski function generalized by the polytope uncertain sets. Moreover, we also investigate robust global error bounds for this uncertain piecewise linear inequality system when the uncertain polytope sets are symmetric sets.

Keywords

• uncertain inequality systems
• error bound
• polytope uncertain set