mlsanityData to 7 Oct 2026

A geometric alternative to Nesterov's accelerated gradient descent

arXiv 1506.08187 ↗First posted 26 Jun 2015math.OC cs.DS cs.LGcited by 21

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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.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Jun 2015.

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Citing papers per year: 2021: 8; 2022: 5; 2023: 3; 2024: 3; 2025: 1; 2026: 1.

21 papers.

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  1. 2021No-Regret Dynamics in the Fenchel Game: A Unified Framework for Algorithmic Convex Optimizationcited by 20
  2. 2021Algorithmic Instabilities of Accelerated Gradient Descentcited by 16
  3. 2021A Continuized View on Nesterov Acceleration for Stochastic Gradient Descent and Randomized Gossipcited by 15
  4. 2021Contextual Recommendations and Low-Regret Cutting-Plane Algorithmscited by 14
  5. 2021Acceleration via Fractal Learning Rate Schedulescited by 13
  6. 2022On the fast convergence of minibatch heavy ball momentumcited by 11
  7. 2021Convergence and Stability of the Stochastic Proximal Point Algorithm with Momentumcited by 7
  8. 2021Fast quantum state reconstruction via accelerated non-convex programmingcited by 5
  9. 2024Accelerated Preference Optimization for Large Language Model Alignmentcited by 5
  10. 2021Potential Function-based Framework for Making the Gradients Small in Convex and Min-Max Optimizationcited by 4
  11. 2025CyclicReflex: Improving Reasoning Models via Cyclical Reflection Token Schedulingcited by 4
  12. 2022Analysis of Dual-Based PID Controllers through Convolutional Mirror Descentcited by 3
9 more
  1. 2023Memory-Constrained Algorithms for Convex Optimization via Recursive Cutting-Planescited by 3
  2. 2023Diffusion Sampling with Momentum for Mitigating Divergence Artifactscited by 3
  3. 2022Understanding A Class of Decentralized and Federated Optimization Algorithms: A Multi-Rate Feedback Control Perspectivecited by 2
  4. 2024Faster Acceleration for Steepest Descentcited by 1
  5. 2022Accelerated Gradient Flow: Risk, Stability, and Implicit Regularizationcited by 0
  6. 2022Learning to Accelerate by the Methods of Step-size Planningcited by 0
  7. 2023Understanding Accelerated Gradient Methods: Lyapunov Analyses and Hamiltonian Assisted Interpretationscited by 0
  8. 2024Generalized Continuous-Time Models for Nesterov's Accelerated Gradient Methodscited by 0
  9. 2026Perfect Parallelization in Mini-Batch SGD with Classical Momentum Accelerationcited by 0