In this paper, we are concerned with the stability of the error bounds for semi-infinite convex constraint systems. Roughly speaking, the error bound of a system of inequalities is said to be stable if all its "small" perturbations admit a (local or global) error bound. We first establish subdifferential characterizations of the stability of error bounds for semi-infinite systems of convex inequalities. By applying these characterizations, we extend some results established by Az\'e and Corvellec on the sensitivity analysis of Hoffman constants to semi-infinite linear constraint systems.
Published in SIAM Journal on Optimization 20 (2010), no. 4, 2080-2096. The original publication is available at http://link.aip.org/link/?SJE/20/2080