Subdifferential Conditions for Calmness of Convex Constraints

We study subdifferential conditions of the calmness property for multifunctions representing convex constraint systems in a Banach space. Extending earlier work in finite dimensions [R. Henrion and J. Outrata, J. Math. Anal. Appl., 258 (2001), pp. 110–130], we show that, in contrast to the stronger Aubin property of a multifunction (or metric regularity of its inverse), calmness can be ensured by corresponding weaker constraint qualifications, which are based only on boundaries of subdifferentials and normal cones rather than on the full objects. Most of the results can be immediately interpreted in the context of error bounds.