Accelerated Gradient Methods for Nonconvex Optimization: Escape Trajectories From Strict Saddle Points and Convergence to Local Minima

arXiv:2307.07030 · math.OC, cs.LG, cs.SY, eess.SY · Submitted 2023-07-13 · Read on arXiv

math.OC, cs.LG, cs.SY, eess.SY

Submitted: 2023-07-13

Updated: 2026-10-16

Comments: 124 pages, 9 figures; adds a short clarification to the proof of Theorem 7.7 and incorporates a proof-stage typo fix; includes additional corrections and clarifications to the version published in Foundations of Computational Mathematics, April 2026

Journal ref: Foundations of Computational Mathematics, April 2026

DOI: 10.1007/s10208-026-09745-x

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Non-asymptotic Analysis — 1× in this paper · explained in 2 episodes

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