  In this paper, based on basic constraint qualification (BCQ) and strong BCQ
for convex generalized equation, we are inspired to further discuss constraint
qualifications of BCQ and strong BCQ for nonconvex generalized equation and
then establish their various characterizations. As applications, we use these
constraint qualifications to study metric subregularity of nonconvex
generalized equation and provide necessary and/or sufficient conditions in
terms of constraint qualifications considered herein to ensure nonconvex
generalized equation having metric subregularity.

Optimization and Control