# Accelerated Methods for α-Weakly-Quasi-Convex Problems

arXiv: https://arxiv.org/abs/1710.00797 · HTML: https://mlsanity.com/paper/1710.00797/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2017.

## Built on by (most cited first, 7 of 7)

- [Nesterov acceleration in benignly non-convex landscapes](https://mlsanity.com/paper/2410.08395/) (2024)
- [Expected Variational Inequalities](https://mlsanity.com/paper/2502.18605/) (2025)
- [Accelerated Policy Gradient: On the Convergence Rates of the Nesterov Momentum for Reinforcement Learning](https://mlsanity.com/paper/2310.11897/) (2023)
- [Demystifying SGD with Doubly Stochastic Gradients](https://mlsanity.com/paper/2406.00920/) (2024)
- [Smooth Quasar-Convex Optimization with Constraints](https://mlsanity.com/paper/2510.01943/) (2025)
- [Adaptive Conditional Gradient Descent](https://mlsanity.com/paper/2510.11440/) (2025)
- [Online Non-Stationary Stochastic Quasar-Convex Optimization](https://mlsanity.com/paper/2407.03601/) (2024)

## Abstract (arXiv)

We provide a quick overview of the class of α-weakly-quasi-convex problems and its relationships with other problem classes. We show that the previously known Sequential Subspace Optimization method retains its optimal convergence rate when applied to minimization problems with smooth α-weakly-quasi-convex objectives. We also show that Nemirovski's conjugate gradients method of strongly convex minimization achieves its optimal convergence rate under weaker conditions of α-weak-quasi-convexity and quad-ratic growth. Previously known results only capture the special case of 1-weak-quasi-convexity or give convergence rates with worse dependence on the parameter α.