Robust Farkas-Minkowski Constraint Qualification for Convex Inequality System Under Data Uncertainty

The Farkas-Minkowski constraint qualification is an important concept within the theory and applications of mathematical programs with inequality constraints. In this paper, we mainly deal with the robust version of Farkas-Minkowski constraint qualification for convex inequality system under data uncertainty. We prove that the existence of robust global error bound is a sufficient condition for ensuring robust Farkas-Minkowski constraint qualification for convex inequality system in face of data uncertainty, where the uncertain data belong to a prescribed compact and convex uncertainty set. Moreover, we show that the converse is true for convex quadratic inequality system, when the uncertain data belong to a scenario uncertainty set.