Olikier–Waldspurger open question on proximal-gradient cluster points
Let be a possibly nonconvex, nonsmooth objective, and let be a sequence generated by a proximal-gradient method for minimizing , with one component locally Lipschitz smooth, as in the setting of Olikier–Waldspurger. Must every cluster point of be a proximal stationary point, namely satisfy the proximal-stationarity condition ?
References
Primary source
Progress summary
A new, unrefereed preprint claims to settle the question about whether proximal-gradient methods have suitably stationary cluster points.
The question was raised by Olikier and Waldspurger in their 2025 SIAM Journal on Optimization paper. It asks for convergence and stationarity guarantees for cluster points of proximal-gradient methods in nonsmooth, nonconvex optimization.
September 2026 affirmative preprint
A new preprint, “Asymptotic Analysis of Gradient Mapping-type Stationarity Measure for the Sum of Nonconvex Nonsmooth Functions and Applications to Proximal Gradient-type Algorithms,” claims an affirmative answer and develops a related stationarity framework. The claim is currently unverified because the preprint is unrefereed.
Current status (as of September 2026): The question is claimed solved by a new unrefereed preprint, but the affirmative result has not been independently verified.
Sources
- arxiv.org
- arxiv.org
- proceedings.mlr.press
- hal.science
- stat.cmu.edu
- opt-ml.org
- deepmind.google
- quantamagazine.org
- deepmind.google
- arxiv.org
- arxiv.org
- arxiv.org
- arxiv.org
- arxiv.org
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- community.openai.com
- cdn.openai.com
- cdn.openai.com
- deepmind.google
Solutions 0
No solutions have been posted yet.