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

By Dmitriy Drusvyatskiy, Boris S. Mordukhovich, Tran Thai An Nghia. 2013

97 citations recorded by the source corpus.

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).

Subfields: Control and Systems Engineering, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f039761eee0e491aefa866750f5e97523bd94b35

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Dmitriy Drusvyatskiy
2. A. S. Lewis

In Geometry and Topology

1. Dmitriy Drusvyatskiy
2. A. S. Lewis
3. Jérôme Bolte

In Mathematical Physics

1. Dmitriy Drusvyatskiy
2. A. S. Lewis

Citations in the corpus

• Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods (2016, background): “We aim to show that the error bound property is equivalent to subregularity of the subdifferential ∂φ itself – a transparent notion closely tied to quadratic growth [15, 17, 19].”