Necessary optimality and suboptimality conditions for nonsmooth problems

The paper aims to develop some basic tools of nonconvex variational analysis with applications to necessary suboptimality and optimality conditions for constrained optimization problems in infinite dimensions. We establish a certain subdifferential variational principle as a new characterization of Asplund spaces and reveal the so-called sequential normal compactness properties of constraint sets that play an essential role in an infinite-dimensional variational analysis and its applications. In light of these tools we obtain new necessary conditions for suboptimal and optimal solutions in general nonsmooth optimization problems with equality, inequality, and set constraints in Asplund spaces.