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

TL;DR

This paper explores the deep connections between second-order growth, tilt stability, and metric regularity of subdifferentials, advancing the theoretical understanding of variational analysis in finite and infinite-dimensional spaces.

Contribution

It establishes new relationships linking second-order growth conditions, metric regularity, tilt stability, and properties of the second-order subdifferential, enhancing the theoretical framework.

Findings

New relationships between second-order growth and metric regularity.

Characterization of tilt stability via second-order subdifferential properties.

Applicability to both finite and infinite-dimensional variational problems.

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).