# Quadratic growth and critical point stability of semi-algebraic functions

arXiv: https://arxiv.org/abs/1309.1446 · HTML: https://mlsanity.com/paper/1309.1446/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2013.

## Built on by (most cited first, 1 of 1)

- [Polyak's Heavy Ball Method Achieves Accelerated Local Rate of Convergence under Polyak-Lojasiewicz Inequality](https://mlsanity.com/paper/2410.16849/) (2024)

## Abstract (arXiv)

We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential --- a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting. As a consequence, we derive necessary conditions and sufficient conditions for optimality in subdifferential terms.