# Complexity of finding near-stationary points of convex functions stochastically

arXiv: https://arxiv.org/abs/1802.08556 · HTML: https://mlsanity.com/paper/1802.08556/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2018.

## Built on by (most cited first, 4 of 4)

- [Oracle Complexity of Single-Loop Switching Subgradient Methods for Non-Smooth Weakly Convex Functional Constrained Optimization](https://mlsanity.com/paper/2301.13314/) (2023)
- [On the Complexity of Finding Small Subgradients in Nonsmooth Optimization](https://mlsanity.com/paper/2209.10346/) (2022)
- [Practical Schemes for Finding Near-Stationary Points of Convex Finite-Sums](https://mlsanity.com/paper/2105.12062/) (2021)
- [Causal Invariance Learning via Efficient Nonconvex Optimization](https://mlsanity.com/paper/2412.11850/) (2024)

## Abstract (arXiv)

In a recent paper, we showed that the stochastic subgradient method applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate O(k-1/4). In this supplementary note, we present a stochastic subgradient method for minimizing a convex function, with the improved rate widetilde O(k-1/2).