  In this paper, we mainly study metric subregularity for a convex constraint
system defined by a convex set-valued mapping and a convex constraint subset.
The main work is to provide several primal equivalent conditions for metric
subregularity by contingent cone and graphical derivative. Further it is proved
that these primal equivalent conditions can characterize strong basic
constraint qualification of convex constraint system given by Zheng and Ng
[SIAM J. Optim., 18(2007), pp. 437-460].
