  In this paper, we study constraint qualifications for the nonconvex
inequality defined by a proper lower semicontinuous function. These constraint
qualifications involve the generalized construction of normal cones and
subdifferentials. Several conditions for these constraint qualifications are
also provided therein. When restricted to the convex inequality, these
constraint qualifications reduce to basic constraint qualification (BCQ) and
strong BCQ studied in [SIAM J. Optim., 14(2004), 757-772] and [Math. Oper.
Res., 30 (2005), 956-965].
