In this paper we study various asymptotic constraint qualifications for the
existence of global error bounds for approximate solutions of convex inequ
alities. Many known conditions that ensure the existence of such a global e
rror bound are shown to be equivalent to one of the following three conditi
ons: (i) the bounded excess condition, (ii) Slater condition together with
the asymptotic constraint qualification defined by Auslender and Crouzeix [
1], and (iii) positivity of normal directional derivatives of the maximum o
f the constraint functions introduced by Lewis and Pang [12].