# The Mirror-Prox Sliding Method for Non-smooth decentralized saddle-point problems

arXiv: https://arxiv.org/abs/2210.06086 · HTML: https://mlsanity.com/paper/2210.06086/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2022.

## Built on by (most cited first, 1 of 1)

- [Accelerated Methods with Complexity Separation Under Data Similarity for Federated Learning Problems](https://mlsanity.com/paper/2601.08614/) (2026)

## Abstract (arXiv)

The saddle-point optimization problems have a lot of practical applications. This paper focuses on such non-smooth problems in decentralized case. This work contains generalization of recently proposed sliding for centralized problem. Through specific penalization method and this sliding we obtain algorithm for non-smooth decentralized saddle-point problems. Note, the proposed method approaches lower bounds both for number of communication rounds and calls of (sub-)gradient per node.