# Solving Nonconvex-Nonconcave Min-Max Problems exhibiting Weak Minty Solutions

arXiv: https://arxiv.org/abs/2201.12247 · HTML: https://mlsanity.com/paper/2201.12247/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2022.

## Built on by (most cited first, 27 of 27)

- [Accelerated Single-Call Methods for Constrained Min-Max Optimization](https://mlsanity.com/paper/2210.03096/) (2022)
- [Solving stochastic weak Minty variational inequalities without increasing batch size](https://mlsanity.com/paper/2302.09029/) (2023)
- [Accelerated Algorithms for Constrained Nonconvex-Nonconcave Min-Max Optimization and Comonotone Inclusion](https://mlsanity.com/paper/2206.05248/) (2022)
- [Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient](https://mlsanity.com/paper/2301.04431/) (2023)
- [Clipped Stochastic Methods for Variational Inequalities with Heavy-Tailed Noise](https://mlsanity.com/paper/2206.01095/) (2022)
- [Single-Call Stochastic Extragradient Methods for Structured Non-monotone Variational Inequalities: Improved Analysis under Weaker Conditions](https://mlsanity.com/paper/2302.14043/) (2023)
- [Universal Gradient Descent Ascent Method for Nonconvex-Nonconcave Minimax Optimization](https://mlsanity.com/paper/2212.12978/) (2022)
- [Beyond the Golden Ratio for Variational Inequality Algorithms](https://mlsanity.com/paper/2212.13955/) (2022)
- [Randomized Block-Coordinate Optimistic Gradient Algorithms for Root-Finding Problems](https://mlsanity.com/paper/2301.03113/) (2023)
- [Worst-case generation via minimax optimization in Wasserstein space](https://mlsanity.com/paper/2512.08176/) (2025)
- [Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developments](https://mlsanity.com/paper/2303.17192/) (2023)
- [Expected Variational Inequalities](https://mlsanity.com/paper/2502.18605/) (2025)
- [Communication-Efficient Gradient Descent-Accent Methods for Distributed Variational Inequalities: Unified Analysis and Local Updates](https://mlsanity.com/paper/2306.05100/) (2023)
- [Revisiting Inexact Fixed-Point Iterations for Min-Max Problems: Stochasticity and Structured Nonconvexity](https://mlsanity.com/paper/2402.05071/) (2024)
- [Extragradient Method for (L0, L1)-Lipschitz Root-finding Problems](https://mlsanity.com/paper/2510.22421/) (2025)
- [Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions](https://mlsanity.com/paper/2603.15576/) (2026)
- [Diffusion Stochastic Optimization for Min-Max Problems](https://mlsanity.com/paper/2401.14585/) (2024)
- [How to Make the Gradient Mapping Small for Constrained Stochastic Min-Max Problems and Beyond](https://mlsanity.com/paper/2609.08380/) (2026)
- [An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problems](https://mlsanity.com/paper/2310.15448/) (2023)
- [Convergence of the Chambolle-Pock Algorithm in the Absence of Monotonicity](https://mlsanity.com/paper/2312.06540/) (2023)
- [A first-order method for nonconvex-nonconcave minimax problems under a local Kurdyka-Lojasiewicz condition](https://mlsanity.com/paper/2507.01932/) (2025)
- [Parameter-Free Non-Ergodic Extragradient Algorithms for Solving Monotone Variational Inequalities](https://mlsanity.com/paper/2604.07662/) (2026)
- [Iterative Minimax Games with Coupled Linear Constraints](https://mlsanity.com/paper/2212.04672/) (2022)
- [Extragradient-Type Methods with O (1/k) Last-Iterate Convergence Rates for Co-Hypomonotone Inclusions](https://mlsanity.com/paper/2302.04099/) (2023)
- [A first-order method for constrained nonconvex-nonconcave minimax optimization](https://mlsanity.com/paper/2510.01168/) (2025)
- [Non-Convex Sparse Reinforcement Learning via Non-Monotone Inclusions](https://mlsanity.com/paper/2607.04990/) (2026)
- [On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalities](https://mlsanity.com/paper/2608.06182/) (2026)

## Abstract (arXiv)

We investigate a structured class of nonconvex-nonconcave min-max problems exhibiting so-called weak Minty solutions, a notion which was only recently introduced, but is able to simultaneously capture different generalizations of monotonicity. We prove novel convergence results for a generalized version of the optimistic gradient method (OGDA) in this setting, matching the 1/k rate for the best iterate in terms of the squared operator norm recently shown for the extragradient method (EG). In addition we propose an adaptive step size version of EG, which does not require knowledge of the problem parameters.