Study of the behaviour of Nesterov accelerated gradient in a non convex setting: the strongly quasar convex case
Abstract
We study the convergence of Nesterov Accelerated Gradient (NAG) minimization algorithm applied to a class of non convex functions called strongly quasar convex functions. We show that NAG 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 that negative friction may appear, the solution of the system achieves an accelerated rate of convergence to the minimum. Finally, we identify the key geometrical property that, if dropped, theoretically cancels the acceleration phenomenon.
Fields of Study & Subjects
Optimization and Variational Analysis
Turtle Biology and Conservation
Sparse and Compressive Sensing Techniques
Publication details
- Journal / source
- Optimization
- Publisher
- Informa UK Limited
- Pages
- 1–26
- Publication date
- 5 June 2026
- Language
- EN