mlsanityData to 7 Oct 2026

Near-optimal method for highly smooth convex optimization

arXiv 1812.08026 ↗First posted 19 Dec 2018math.OCcited by 16

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Abstract (arXiv)

We propose a near-optimal method for highly smooth convex optimization. More precisely, in the oracle model where one obtains the pth order Taylor expansion of a function at the query point, we propose a method with rate of convergence tildeO(1/k^frac 3p +12) after k queries to the oracle for any convex function whose pth order derivative is Lipschitz.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Dec 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 1; 2023: 4; 2024: 4; 2025: 2; 2026: 2.

16 papers.

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  1. 2022The First Optimal Acceleration of High-Order Methods in Smooth Convex Optimizationcited by 19
  2. 2021Acceleration via Fractal Learning Rate Schedulescited by 13
  3. 2021Near-Optimal Lower Bounds For Convex Optimization For All Orders of Smoothnesscited by 6
  4. 2023Debiasing Conditional Stochastic Optimizationcited by 6
  5. 2024Proximal Oracles for Optimization and Samplingcited by 5
  6. 2023Accelerated Quasi-Newton Proximal Extragradient: Faster Rate for Smooth Convex Optimizationcited by 4
  7. 2021Understanding Riemannian Acceleration via a Proximal Extragradient Frameworkcited by 3
  8. 2023Higher-Order Newton Methods with Polynomial Work per Iterationcited by 3
  9. 2023A Whole New Ball Game: A Primal Accelerated Method for Matrix Games and Minimizing the Maximum of Smooth Functionscited by 3
  10. 2024Tight Lower Bounds under Asymmetric High-Order H"older Smoothness and Uniform Convexitycited by 3
  11. 2024Non-Euclidean High-Order Smooth Convex Optimizationcited by 3
  12. 2024Faster Acceleration for Steepest Descentcited by 1
4 more
  1. 2025Solving Convex-Concave Problems with tildeO(ε-4/7) Second-Order Oracle Complexitycited by 0
  2. 2025Simple Stepsize for Quasi-Newton Methods with Global Convergence Guaranteescited by 0
  3. 2026Halpern Iteration Achieves tildeO(ε-1/p) pth-Order Oracle Complexity for Monotone Variational Inequalitiescited by 0
  4. 2026Optimal High-Order Methods for Solving Monotone Variational Inequalitiescited by 0