Reachability of gradient descent
Optimization and Control
2026-02-27 v2
Abstract
We show that gradient descent can converge to any local minimum of a smooth semi-algebraic function. This holds if the step sizes are nonsummable and sufficiently small. The same results hold for the subgradient method on locally Lipschitz semi-algebraic functions if the step size is constant.
Cite
@article{arxiv.2509.12165,
title = {Reachability of gradient descent},
author = {Cédric Josz and Wenqing Ouyang},
journal= {arXiv preprint arXiv:2509.12165},
year = {2026}
}
Comments
16 pages