Year: 2026
Type: preprint
Abstract: We construct a coercive, locally Lipschitz, semialgebraic function on $\mathbb R^2$ for which BFGS with Armijo--Wolfe line search converges to a non-Clarke-stationary point from a nonempty open set of initial points and inverse-Hessian estimates. This disproves the almost-sure stationarity assertion in the 2013 challenge of Lewis and Overton. The construction and proof combine analytical arguments with computer-assisted verification of explicit inequalities.
Source: arXiv (Cornell University)
Author: Lai, Lexiao
Institution: University of Hong Kong
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223959273