# A Proof of the Exact Convergence Rate of Gradient Descent

arXiv: https://arxiv.org/abs/2412.04427 · HTML: https://mlsanity.com/paper/2412.04427/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2024.

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

- [A lower bound for stepsize-based acceleration of gradient descent](https://mlsanity.com/paper/2608.10418/) (2026)

## Abstract (arXiv)

We prove the exact worst-case convergence rate of gradient descent for smooth strongly convex optimization on ℝd. Concretely, assuming that the objective function f is μ-strongly convex and L-smooth, we identify the smallest possible value of τ for which the inequality f(xN)-f*≤τ|x0-x*|2 always holds. The result was previously conjectured by Drori and Teboulle for the case μ=0, and by Taylor, Hendrickx, and Glineur for the case μ>0.