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Primal-dual subgradient methods for minimizing uniformly convex functions

arXiv 1401.1792 ↗First posted 8 Jan 2014math.OCcited by 11

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Abstract (arXiv)

We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are adaptive with respect to the parameters of strong or uniform convexity of the objective: in the case when the total number of iterations N is fixed, their accuracy coincides, up to a logarithmic in N factor with the accuracy of optimal algorithms.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Jan 2014.

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

11 papers.

  1. 2022Making SGD Parameter-Freecited by 50
  2. 2021Stochastic Mirror Descent: Convergence Analysis and Adaptive Variants via the Mirror Stochastic Polyak Stepsizecited by 22
  3. 2022Mirror Descent Strikes Again: Optimal Stochastic Convex Optimization under Infinite Noise Variancecited by 22
  4. 2021Adapting to Function Difficulty and Growth Conditions in Private Optimizationcited by 19
  5. 2022Fast Composite Optimization and Statistical Recovery in Federated Learningcited by 12
  6. 2021Local and Global Uniform Convexity Conditionscited by 4
  7. 2024Stochastic Online Optimization for Cyber-Physical and Robotic Systemscited by 3
  8. 2024Tight Lower Bounds under Asymmetric High-Order H"older Smoothness and Uniform Convexitycited by 3
  9. 2023Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methodscited by 2
  10. 2025On the necessity of adaptive regularisation:Optimal anytime online learning on boldsymbolℓp-ballscited by 1
  11. 2026Bilevel Optimization with Lower-Level Uniform Convexity: Theory and Algorithmcited by 0