  This paper is devoted to second-order variational analysis of a rather broad
class of extended-real-valued piecewise liner functions and their applications
to various issues of optimization and stability. Based on our recent explicit
calculations of the second-order subdifferential for such functions, we
establish relationships between nondegeneracy and second-order qualification
for fully amenable compositions involving piecewise linear functions. We then
provide a second-order characterization of full stable local minimizers in
composite optimization and constrained minimax problems.
