# Primal subgradient methods with predefined stepsizes

arXiv: https://arxiv.org/abs/2311.13838 · HTML: https://mlsanity.com/paper/2311.13838/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2023.

## Built on by (most cited first, 2 of 2)

- [DADA: Dual Averaging with Distance Adaptation](https://mlsanity.com/paper/2501.10258/) (2025)
- [Gradient-Normalized Smoothness for Optimization with Approximate Hessians](https://mlsanity.com/paper/2506.13710/) (2025)

## Abstract (arXiv)

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal value of the objective function, need corrections when they are applied to optimization problems with constraints. Their proper modifications allow a significant acceleration of these schemes when the objective function has favorable properties (smoothness, strong convexity). We show how the new methods can be used for solving optimization problems with functional constraints with possibility to approximate the optimal Lagrange multipliers. One of our primal-dual methods works also for unbounded feasible set.