# A geometric alternative to Nesterov's accelerated gradient descent

arXiv: https://arxiv.org/abs/1506.08187 · HTML: https://mlsanity.com/paper/1506.08187/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2015.

## Built on by (most cited first, 22 of 22)

- [No-Regret Dynamics in the Fenchel Game: A Unified Framework for Algorithmic Convex Optimization](https://mlsanity.com/paper/2111.11309/) (2021)
- [Algorithmic Instabilities of Accelerated Gradient Descent](https://mlsanity.com/paper/2102.02167/) (2021)
- [Contextual Recommendations and Low-Regret Cutting-Plane Algorithms](https://mlsanity.com/paper/2106.04819/) (2021)
- [A Continuized View on Nesterov Acceleration for Stochastic Gradient Descent and Randomized Gossip](https://mlsanity.com/paper/2106.07644/) (2021)
- [Acceleration via Fractal Learning Rate Schedules](https://mlsanity.com/paper/2103.01338/) (2021)
- [On the fast convergence of minibatch heavy ball momentum](https://mlsanity.com/paper/2206.07553/) (2022)
- [Convergence and Stability of the Stochastic Proximal Point Algorithm with Momentum](https://mlsanity.com/paper/2111.06171/) (2021)
- [Fast quantum state reconstruction via accelerated non-convex programming](https://mlsanity.com/paper/2104.07006/) (2021)
- [Accelerated Preference Optimization for Large Language Model Alignment](https://mlsanity.com/paper/2410.06293/) (2024)
- [CyclicReflex: Improving Reasoning Models via Cyclical Reflection Token Scheduling](https://mlsanity.com/paper/2506.11077/) (2025)
- [Potential Function-based Framework for Making the Gradients Small in Convex and Min-Max Optimization](https://mlsanity.com/paper/2101.12101/) (2021)
- [Analysis of Dual-Based PID Controllers through Convolutional Mirror Descent](https://mlsanity.com/paper/2202.06152/) (2022)
- [Memory-Constrained Algorithms for Convex Optimization via Recursive Cutting-Planes](https://mlsanity.com/paper/2306.10096/) (2023)
- [Diffusion Sampling with Momentum for Mitigating Divergence Artifacts](https://mlsanity.com/paper/2307.11118/) (2023)
- [Understanding A Class of Decentralized and Federated Optimization Algorithms: A Multi-Rate Feedback Control Perspective](https://mlsanity.com/paper/2204.12663/) (2022)
- [Faster Acceleration for Steepest Descent](https://mlsanity.com/paper/2409.19200/) (2024)
- [Accelerated Gradient Flow: Risk, Stability, and Implicit Regularization](https://mlsanity.com/paper/2201.08311/) (2022)
- [Learning to Accelerate by the Methods of Step-size Planning](https://mlsanity.com/paper/2204.01705/) (2022)
- [Understanding Accelerated Gradient Methods: Lyapunov Analyses and Hamiltonian Assisted Interpretations](https://mlsanity.com/paper/2304.10063/) (2023)
- [Generalized Continuous-Time Models for Nesterov's Accelerated Gradient Methods](https://mlsanity.com/paper/2409.00913/) (2024)
- [Perfect Parallelization in Mini-Batch SGD with Classical Momentum Acceleration](https://mlsanity.com/paper/2605.18609/) (2026)
- [Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time](https://mlsanity.com/paper/2606.17260/) (2026)

## Abstract (arXiv)

We propose a new method for unconstrained optimization of a smooth and strongly convex function, which attains the optimal rate of convergence of Nesterov's accelerated gradient descent. The new algorithm has a simple geometric interpretation, loosely inspired by the ellipsoid method. We provide some numerical evidence that the new method can be superior to Nesterov's accelerated gradient descent.