# About some works of Boris Polyak on convergence of gradient methods and their development

arXiv: https://arxiv.org/abs/2311.16743 · HTML: https://mlsanity.com/paper/2311.16743/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [Large Deviation Upper Bounds and Improved MSE Rates of Nonlinear SGD: Heavy-tailed Noise and Power of Symmetry](https://mlsanity.com/paper/2410.15637/) (2024)

## Abstract (arXiv)

The paper presents a review of the state-of-the-art of subgradient and accelerated methods of convex optimization, including in the presence of disturbances and access to various information about the objective function (function value, gradient, stochastic gradient, higher derivatives). For nonconvex problems, the Polak-Lojasiewicz condition is considered and a review of the main results is given. The behavior of numerical methods in the presence of sharp minima is considered. The purpose of this survey is to show the influence of the works of B.T. Polyak (1935 -- 2023) on gradient optimization methods and their neighborhoods on the modern development of numerical optimization methods.