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

D. Drusvyatskiy(dd379cornell.edu)
B.S. Mordukhovich(borismath.wayne.edu)
T.T.A. Nghia(nghiamath.wayne.edu)

Abstract: 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).

Keywords: variational analysis, quadratic growth, first-order and second-order generalized differentiation, metric regularity and subregularity, prox-regular functions, tilt stability in optimization

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: 23 pages, April 2013

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Entry Submitted: 04/27/2013
Entry Accepted: 04/28/2013
Entry Last Modified: 04/27/2013

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