Metric regularity and constraint qualifications for convex inequalities on Banach spaces

We introduce new notions of the extended basic constraint qualification and the strong basic constraint qualification and discuss their relationship with other fundamental concepts such as the basic constraint quali. cation and the metric regularity; in particular we provide a solution to an open problem of Lewis and Pangon characterizing the metric regularity in terms of normal cones. We present a characterization of error bounds for convex inequalities in terms of the strong basic constraint quali. cation. As applications, we study the linear regularity for infinite collections of closed convex sets in a Banach space.