# Primal-dual subgradient methods for minimizing uniformly convex functions

arXiv: https://arxiv.org/abs/1401.1792 · HTML: https://mlsanity.com/paper/1401.1792/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2014.

## Built on by (most cited first, 11 of 11)

- [Making SGD Parameter-Free](https://mlsanity.com/paper/2205.02160/) (2022)
- [Mirror Descent Strikes Again: Optimal Stochastic Convex Optimization under Infinite Noise Variance](https://mlsanity.com/paper/2202.11632/) (2022)
- [Stochastic Mirror Descent: Convergence Analysis and Adaptive Variants via the Mirror Stochastic Polyak Stepsize](https://mlsanity.com/paper/2110.15412/) (2021)
- [Adapting to Function Difficulty and Growth Conditions in Private Optimization](https://mlsanity.com/paper/2108.02391/) (2021)
- [Fast Composite Optimization and Statistical Recovery in Federated Learning](https://mlsanity.com/paper/2207.08204/) (2022)
- [Stochastic Online Optimization for Cyber-Physical and Robotic Systems](https://mlsanity.com/paper/2404.05318/) (2024)
- [Local and Global Uniform Convexity Conditions](https://mlsanity.com/paper/2102.05134/) (2021)
- [Tight Lower Bounds under Asymmetric High-Order H"older Smoothness and Uniform Convexity](https://mlsanity.com/paper/2409.10773/) (2024)
- [Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methods](https://mlsanity.com/paper/2301.02268/) (2023)
- [On the necessity of adaptive regularisation:Optimal anytime online learning on boldsymbolℓp-balls](https://mlsanity.com/paper/2506.19752/) (2025)
- [Bilevel Optimization with Lower-Level Uniform Convexity: Theory and Algorithm](https://mlsanity.com/paper/2603.00027/) (2026)

## 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.