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

Department of Mathematics, University of Washington, Seattle, WA 98195, USA
and: 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

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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. https://doi.org/10.68381/jca21061

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press LLC.