  This paper sheds new light on several interrelated topics of second-order
variational analysis, both in finite and infinite-dimensional settings. We
establish new relationships between second-order growth conditions on
functions, the basic properties of metric regularity and subregularity of the
limiting subdifferential, tilt-stability of local minimizers, and
positive-definiteness/semidefiniteness properties of the second-order
subdifferential (or generalized Hessian).
