# Universal fast gradient method for stochastic composit optimization problems

arXiv: https://arxiv.org/abs/1604.05275 · HTML: https://mlsanity.com/paper/1604.05275/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2016.

## Built on by (most cited first, 2 of 2)

- [Breaking the Heavy-Tailed Noise Barrier in Stochastic Optimization Problems](https://mlsanity.com/paper/2311.04161/) (2023)
- [Nesterov Finds GRAAL: Optimal and Adaptive Gradient Method for Convex Optimization](https://mlsanity.com/paper/2507.09823/) (2025)

## Abstract (arXiv)

We propose a new simple variant of Fast Gradient Method that requires only one projection per iteration. We called this method Triangle Method (TM) because it has a corresponding geometric description. We generalize TM for convex and strictly convex composite optimization problems. Then we propose Universal Triangle Method (UTM) for convex and strictly convex composite optimization problems (see Yu. Nesterov, Math. Program. 2015. for more details about what is Universal Fast Gradient Method). Finally, based on mini-batch technique we propose Stochastic Universal Triangle Method (SUTM). SUTM can be applied to stochastic convex and strictly convex composite optimization problems. Denote, that all the methods TM, UTM, SUTM are continuous on strictly convexity parameter and all of them reach known lower bounds. With additional assumption about the structure of the problems these methods work better than the lower bounds.