Second-Order Growth, Tilt Stability, and Metric Regularity of the Subdifferential

Dmitriy Drusvyatskiy; Boris S. Mordukhovich; Tran T. A. Nghia

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).

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

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

Mathematics Subject Classification

49J52, 49J53, 90C31

Suggested citation

D. Drusvyatskiy, B. S. Mordukhovich, T. T. A. Nghia. “Second-Order Growth, Tilt Stability, and Metric Regularity of the Subdifferential.” Journal of Convex Analysis 21 (2014), No. 4, 1165–1192.