Journal of Convex Analysis 21 (2014), No. 4, 1165--1192
Copyright Heldermann Verlag 2014
Second-Order Growth, Tilt Stability, and Metric Regularity of the Subdifferential
Dmitriy Drusvyatskiy
Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
ddrusvya@uwaterloo.ca
Boris S. Mordukhovich
Dept. of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.
boris@math.wayne.edu
Tran T. A. Nghia
Dept. of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.
nghia@math.wayne.edu
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.
MSC: 49J52, 49J53, 90C31
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