# Convergence rate analysis of the gradient descent-ascent method for convex-concave saddle-point problems

arXiv: https://arxiv.org/abs/2209.01272 · HTML: https://mlsanity.com/paper/2209.01272/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2022.

## Built on by (most cited first, 5 of 5)

- [Stackelberg Learning from Human Feedback: Preference Optimization as a Sequential Game](https://mlsanity.com/paper/2512.16626/) (2025)
- [Contractivity and linear convergence in bilinear saddle-point problems: An operator-theoretic approach](https://mlsanity.com/paper/2410.14592/) (2024)
- [Provable Last-Iterate Convergence for Multi-Objective Safe LLM Alignment via Optimistic Primal-Dual](https://mlsanity.com/paper/2602.22146/) (2026)
- [Negative Momentum for Convex-Concave Optimization](https://mlsanity.com/paper/2604.17145/) (2026)
- [Near-Optimal Single-Loop Predictor--Corrector Extragradient Method for Strongly Convex--Strongly Concave Minimax Optimization](https://mlsanity.com/paper/2609.20327/) (2026)

## Abstract (arXiv)

In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming performance estimation method. The given convergence rate incorporates most parameters of the problem and it is exact for a large class of strongly convex-strongly concave saddle-point problems for one iteration. We also investigate the algorithm without strong convexity and we provide some necessary and sufficient conditions under which the gradient descent-ascent enjoys linear convergence.