Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential

TL;DR

This paper demonstrates the fundamental equivalence between three key concepts in optimization—uniform second order growth, tilt stability, and strong metric regularity of the subdifferential—for lower-semicontinuous functions, unifying different theoretical frameworks.

Contribution

It establishes the equivalence of three important notions in variational analysis, bridging gaps between different areas of optimization theory.

Findings

Proves the equivalence of uniform second order growth, tilt stability, and strong metric regularity.

Applies to all lower-semicontinuous, extended-real-valued functions.

Provides a unified understanding of stability concepts in optimization.

Abstract

We prove that uniform second order growth, tilt stability, and strong metric regularity of the limiting subdifferential --- three notions that have appeared in entirely different settings --- are all essentially equivalent for any lower-semicontinuous, extended-real-valued function.