Second-order growth, tilt stability, and metric regularity of the subdifferential

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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).