# Study of the behaviour of Nesterov Accelerated Gradient in a non convex setting: the strongly quasar convex case

arXiv: https://arxiv.org/abs/2405.19809 · HTML: https://mlsanity.com/paper/2405.19809/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2024.

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

- [Nesterov acceleration in benignly non-convex landscapes](https://mlsanity.com/paper/2410.08395/) (2024)
- [Minimisation of Quasar-Convex Functions Using Random Zeroth-Order Oracles](https://mlsanity.com/paper/2505.02281/) (2025)
- [Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs](https://mlsanity.com/paper/2501.00389/) (2024)

## Abstract (arXiv)

We study the convergence of Nesterov Accelerated Gradient (NAG) minimization algorithmapplied to a class of non convex functions called strongly quasar convex functions. We show thatNAG can achieve an accelerated convergence speed at the cost of a lower curvature assumption.We provide a continuous analysis through high resolution ODEs, where we show that despite thatnegative friction may appear, the solution of the system achieves accelerated rate of convergenceto the minimum. Finally, we identify the key geometrical property that, if dropped, theoreticallycancels the acceleration phenomenon.