Calmness and Error Bounds for Convex Constraint Systems
Wen Wu Song · SIAM Journal on Optimization · 2006
In the paper, we first compare the concepts of calmness, local error bound, and locally linear regularity. Second, we present some dual sufficient conditions for local error bound and local linear regularity. By using a characterization of the locally linear regularity for a collection of finite nonempty closed and convex subsets, we prove that the sufficient conditions provided in [R. Henrion and J. Outrata, J. Math. Anal. Appl., 258 (2001), pp. 110-130; R. Henrion and A. Jourani, SIAM J. Optim., 13 (2002), pp. 520-534; R. Henrion, A. Jourani, and J. Outrata, SIAM J. Optim., 13 (2002), pp. 603-618] imply not only the calmness but also the existence of local error bounds for the convex constraint system in an infinite-dimensional setting.