The paper aims to develop some basic principles and 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. This result is different from conventional support forms of variational principles and appears to be convenient for applications to nonsmooth optimization. Based on the subdifferential variational principle, we obtain new necessary conditions for suboptimal solutions in general nonsmooth optimization problems with equality, inequality, and set constraints in Asplund spaces. In this way we establish the so-called sequential normal compactness properties of constraint sets that play an essential role in infinite-dimensional variational analysis and its applications. As a by-product of our approach, we derive various forms of necessary optimality conditions for nonsmooth constrained problems in infinite dimensions, which extend known results in that direction.