# A Note on Nesterov's Accelerated Method in Nonconvex Optimization: a Weak Estimate Sequence Approach

arXiv: https://arxiv.org/abs/2006.08548 · HTML: https://mlsanity.com/paper/2006.08548/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [Continuized Acceleration for Quasar Convex Functions in Non-Convex Optimization](https://mlsanity.com/paper/2302.07851/) (2023)
- [Accelerated Policy Gradient: On the Convergence Rates of the Nesterov Momentum for Reinforcement Learning](https://mlsanity.com/paper/2310.11897/) (2023)
- [A Novel Unified Parametric Assumption for Nonconvex Optimization](https://mlsanity.com/paper/2502.12329/) (2025)

## Abstract (arXiv)

We present a variant of accelerated gradient descent algorithms, adapted from Nesterov's optimal first-order methods, for weakly-quasi-convex and weakly-quasi-strongly-convex functions. We show that by tweaking the so-called estimate sequence method, the derived algorithm achieves optimal convergence rate for weakly-quasi-convex and weakly-quasi-strongly-convex in terms of oracle complexity. In particular, for a weakly-quasi-convex function with Lipschitz continuous gradient, we require O(frac1√varepsilon) iterations to acquire an varepsilon-solution; for weakly-quasi-strongly-convex functions, the iteration complexity is Oleft( lnleft(frac1varepsilonright) right). Furthermore, we discuss the implications of these algorithms for linear quadratic optimal control problem.