  In this paper, we propose second-order sufficient optimality conditions for a
very general nonconvex constrained optimization problem, which covers many
prominent mathematical programs.Unlike the existing results in the literature,
our conditions prove to be sufficient, for an essential local minimizer of
second order, under merely basic smoothness and closedness assumptions on the
data defining the problem.In the second part, we propose a comprehensive first-
and second-order variational analysis of disjunctive systems and demonstrate
how the second-order objects appearing in the optimality conditions can be
effectively computed in this case.
