Publications · Journal article · Found. Comput. Math. 2026
Accelerated gradient methods for nonconvex optimization: escape trajectories from strict saddle points and convergence to local minima
Foundations of Computational Mathematics, 2026.
In brief
Momentum methods are known to escape saddle points of non-convex functions, but how, and how fast? The paper analyzes the trajectories of a family of accelerated gradient methods near strict saddle points, characterizes the time they take to leave as a function of the local geometry, and shows that the methods converge to local minima — with an explicit account of the role the momentum parameter plays in both.
Topics
Cite
@article{dixit2026escape,
title = {Accelerated gradient methods for nonconvex optimization: escape trajectories from strict saddle points and convergence to local minima},
author = {Rishabh Dixit and Mert Gürbüzbalaban and Waheed U. Bajwa},
year = {2026},
journal = {Foundations of Computational Mathematics},
doi = {10.1007/s10208-026-09745-x},
}Relatedsame topics