# Accelerated methods for composite non-bilinear saddle point problem

arXiv: https://arxiv.org/abs/1906.03620 · HTML: https://mlsanity.com/paper/1906.03620/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2019.

## Built on by (most cited first, 6 of 6)

- [Complexity Lower Bounds for Nonconvex-Strongly-Concave Min-Max Optimization](https://mlsanity.com/paper/2104.08708/) (2021)
- [The First Optimal Algorithm for Smooth and Strongly-Convex-Strongly-Concave Minimax Optimization](https://mlsanity.com/paper/2205.05653/) (2022)
- [Convex-Concave Min-Max Stackelberg Games](https://mlsanity.com/paper/2110.05192/) (2021)
- [Sion's Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithm](https://mlsanity.com/paper/2202.06950/) (2022)
- [Minimax Optimization: The Case of Convex-Submodular](https://mlsanity.com/paper/2111.01262/) (2021)
- [Robust No-Regret Learning in Min-Max Stackelberg Games](https://mlsanity.com/paper/2203.14126/) (2022)

## Abstract (arXiv)

Based on G. Lan's accelerated gradient sliding and general relation between the smoothness and strong convexity parameters of function under Legendre transformation we show that under rather general conditions the best known bounds for bilinear convex-concave smooth composite saddle point problem keep true for or non-bilinear convex-concave smooth composite saddle point problem. Moreover, we describe situations when the bounds differ and explain the nature of the difference.