# Semi-Anchored Multi-Step Gradient Descent Ascent Method for Structured Nonconvex-Nonconcave Composite Minimax Problems

arXiv: https://arxiv.org/abs/2105.15042 · HTML: https://mlsanity.com/paper/2105.15042/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2021.

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

- [Escaping limit cycles: Global convergence for constrained nonconvex-nonconcave minimax problems](https://mlsanity.com/paper/2302.09831/) (2023)
- [Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization](https://mlsanity.com/paper/2408.11974/) (2024)
- [Beyond the Golden Ratio for Variational Inequality Algorithms](https://mlsanity.com/paper/2212.13955/) (2022)
- [Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domain](https://mlsanity.com/paper/2110.03950/) (2021)
- [Expected Variational Inequalities](https://mlsanity.com/paper/2502.18605/) (2025)
- [An Improved Last-Iterate Convergence Rate for Anchored Gradient Descent Ascent](https://mlsanity.com/paper/2604.03782/) (2026)

## Abstract (arXiv)

Minimax problems, such as generative adversarial network, adversarial training, and fair training, are widely solved by a multi-step gradient descent ascent (MGDA) method in practice. However, its convergence guarantee is limited. In this paper, inspired by the primal-dual hybrid gradient method, we propose a new semi-anchoring (SA) technique for the MGDA method. This makes the MGDA method find a stationary point of a structured nonconvex-nonconcave composite minimax problem; its saddle-subdifferential operator satisfies the weak Minty variational inequality condition. The resulting method, named SA-MGDA, is built upon a Bregman proximal point method. We further develop its backtracking line-search version, and its non-Euclidean version for smooth adaptable functions. Numerical experiments, including a fair classification training, are provided.