# Pathological subgradient dynamics

arXiv: https://arxiv.org/abs/1910.13604 · HTML: https://mlsanity.com/paper/1910.13604/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2019.

## Built on by (most cited first, 9 of 9)

- [Gradient-Free Methods for Deterministic and Stochastic Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2209.05045/) (2022)
- [Deterministic Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2302.08300/) (2023)
- [Stochastic Subgradient Descent Escapes Active Strict Saddles on Weakly Convex Functions](https://mlsanity.com/paper/2108.02072/) (2021)
- [Adam-family Methods with Decoupled Weight Decay in Deep Learning](https://mlsanity.com/paper/2310.08858/) (2023)
- [Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2404.09438/) (2024)
- [On the Hardness of Meaningful Local Guarantees in Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2409.10323/) (2024)
- [Permutation Randomization on Nonsmooth Nonconvex Optimization: A Theoretical and Experimental Study](https://mlsanity.com/paper/2505.11752/) (2025)
- [Lipschitzian SLLNs for random functions](https://mlsanity.com/paper/2607.20411/) (2026)
- [The Exponential Price of Determinism in Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2609.23837/) (2026)

## Abstract (arXiv)

We construct examples of Lipschitz continuous functions, with pathological subgradient dynamics both in continuous and discrete time. In both settings, the iterates generate bounded trajectories, and yet fail to detect any (generalized) critical points of the function.