This paper studies stability of error bounds for convex constraint systems in Banach spaces. We show that certain known sufficient conditions for local and global error bounds actually ensure error bounds for the family of functions being in a sense small perturbations of the given one. A single inequality as well as semi-infinite constraint systems are considered.
Published in SIAM Journal on Optimization 20 (2010), no. 6, 3280-3296. The original publication is available at http://link.aip.org/link/?SJE/20/3280