# An optimal gradient method for smooth strongly convex minimization

arXiv: https://arxiv.org/abs/2101.09741 · HTML: https://mlsanity.com/paper/2101.09741/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2021.

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

- [Provably Faster Gradient Descent via Long Steps](https://mlsanity.com/paper/2307.06324/) (2023)
- [PEPit: computer-assisted worst-case analyses of first-order optimization methods in Python](https://mlsanity.com/paper/2201.04040/) (2022)
- [Accelerating Value Iteration with Anchoring](https://mlsanity.com/paper/2305.16569/) (2023)
- [Practical Schemes for Finding Near-Stationary Points of Convex Finite-Sums](https://mlsanity.com/paper/2105.12062/) (2021)
- [Memory-Constrained Algorithms for Convex Optimization via Recursive Cutting-Planes](https://mlsanity.com/paper/2306.10096/) (2023)
- [Nesterov Acceleration for Ensemble Kalman Inversion and Variants](https://mlsanity.com/paper/2501.08779/) (2025)
- [Understanding Accelerated Gradient Methods: Lyapunov Analyses and Hamiltonian Assisted Interpretations](https://mlsanity.com/paper/2304.10063/) (2023)

## Abstract (arXiv)

We present an optimal gradient method for smooth strongly convex optimization. The method is optimal in the sense that its worst-case bound on the distance to an optimal point exactly matches the lower bound on the oracle complexity for the class of problems, meaning that no black-box first-order method can have a better worst-case guarantee without further assumptions on the class of problems at hand. In addition, we provide a constructive recipe for obtaining the algorithmic parameters of the method and illustrate that it can be used for deriving methods for other optimality criteria as well.