GLOBAL ERROR-BOUNDS FOR CONVEX INEQUALITY SYSTEMS IN BANACH-SPACES

We study conditions under which a global error bound in terms of a nat ural residual exists for a convex inequality system. Specifically, we obtain an error bound result, which unifies many existing results assu ming a Slater condition. We also derive two characterizations for a co nvex inequality system to possess a global error bound; one is in term s of metric regularity, and the other is in terms of an associated con vex inequality system. As a consequence, we show that in R-n a global error bound holds for such a system under the assumption of the zero v ector in the relative interior of the domain of an associated conjugat e function along with metric regularity at every point of the feasible set defined by the system. Finally, we discuss some applications of t hese results to convex programs.