# A note on the optimal convergence rate of descent methods with fixed step sizes for smooth strongly convex functions

arXiv: https://arxiv.org/abs/2106.08020 · HTML: https://mlsanity.com/paper/2106.08020/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2021.

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

- [Accelerated Evolving Set Processes for Local PageRank Computation](https://mlsanity.com/paper/2510.08010/) (2025)
- [A Closed-Form Upper Bound for Admissible Learning-Rate Steps in Belief-Space Dynamics](https://mlsanity.com/paper/2605.06741/) (2026)

## Abstract (arXiv)

Based on a result by Taylor, Hendrickx, and Glineur (J. Optim. Theory Appl., 178(2):455--476, 2018) on the attainable convergence rate of gradient descent for smooth and strongly convex functions in terms of function values, an elementary convergence analysis for general descent methods with fixed step sizes is presented. It covers general variable metric methods, gradient related search directions under angle and scaling conditions, as well as inexact gradient methods. In all cases, optimal rates are obtained.