Radius of Robust Feasibility of System of Convex Inequalities with Uncertain Data

Abstract

In this paper, we investigate the radius of robust feasibility of system of uncertain convex inequalities by the Minkowski function. We firstly establish an upper bound and a lower bound for radius of robust feasibility of the system of uncertain convex inequalities. Exact formulas of radius of robust feasibility of the system are derived under the nonsymmetric and symmetric assumptions of the uncertain sets. We also obtain a characterization on the positiveness of radius of robust feasibility for the system. Lastly, explicit tractable formulas for computing the radius of robust feasibility of the system are presented when the uncertain sets are ellipsoids, polytopes, boxes and unit ball, respectively.